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	<entry>
		<id>https://wiki.ubc.ca/index.php?title=Thread:Course_talk:MATH110/003/Math_Forum/Homework_13_Part_2_(economics/demand_question)&amp;diff=75040</id>
		<title>Thread:Course talk:MATH110/003/Math Forum/Homework 13 Part 2 (economics/demand question)</title>
		<link rel="alternate" type="text/html" href="https://wiki.ubc.ca/index.php?title=Thread:Course_talk:MATH110/003/Math_Forum/Homework_13_Part_2_(economics/demand_question)&amp;diff=75040"/>
		<updated>2011-02-03T22:25:03Z</updated>

		<summary type="html">&lt;p&gt;AdamsNguyen: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;I don&#039;t even know how to start. I spent 2 hours raging on the question... Help would be kindly appreciated.&lt;br /&gt;
&lt;br /&gt;
http://i749.photobucket.com/albums/xx131/DB81397/FU-.jpg&lt;/div&gt;</summary>
		<author><name>AdamsNguyen</name></author>
	</entry>
	<entry>
		<id>https://wiki.ubc.ca/index.php?title=Thread:Course_talk:MATH110/003/Math_Forum/Homework_13_Part_2_(economics/demand_question)&amp;diff=75039</id>
		<title>Thread:Course talk:MATH110/003/Math Forum/Homework 13 Part 2 (economics/demand question)</title>
		<link rel="alternate" type="text/html" href="https://wiki.ubc.ca/index.php?title=Thread:Course_talk:MATH110/003/Math_Forum/Homework_13_Part_2_(economics/demand_question)&amp;diff=75039"/>
		<updated>2011-02-03T22:24:41Z</updated>

		<summary type="html">&lt;p&gt;AdamsNguyen: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;I don&#039;t even know how to start. I spent 2 hours raging on the question... Help would be kindly appreciated.&lt;br /&gt;
&lt;br /&gt;
[IMG]http://i749.photobucket.com/albums/xx131/DB81397/FU-.jpg[/IMG]&lt;/div&gt;</summary>
		<author><name>AdamsNguyen</name></author>
	</entry>
	<entry>
		<id>https://wiki.ubc.ca/index.php?title=Thread:Course_talk:MATH110/003/Math_Forum/Homework_13_Part_2_(economics/demand_question)&amp;diff=75038</id>
		<title>Thread:Course talk:MATH110/003/Math Forum/Homework 13 Part 2 (economics/demand question)</title>
		<link rel="alternate" type="text/html" href="https://wiki.ubc.ca/index.php?title=Thread:Course_talk:MATH110/003/Math_Forum/Homework_13_Part_2_(economics/demand_question)&amp;diff=75038"/>
		<updated>2011-02-03T22:22:06Z</updated>

		<summary type="html">&lt;p&gt;AdamsNguyen: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;I don&#039;t even know how to start. I spent 2 hours raging on the question... Help would be kindly appreciated.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;nowiki&amp;gt;&amp;lt;img&amp;gt;https://chrome.google.com/webstore/img/ajjgiajaoafimgkdlcofflenackmpjhd/1292196379.87/logo128/1?itemtype=ext&amp;lt;/img&amp;gt;&amp;lt;/nowiki&amp;gt;&lt;/div&gt;</summary>
		<author><name>AdamsNguyen</name></author>
	</entry>
	<entry>
		<id>https://wiki.ubc.ca/index.php?title=Thread:Course_talk:MATH110/003/Math_Forum/Homework_13_Part_2_(economics/demand_question)&amp;diff=75037</id>
		<title>Thread:Course talk:MATH110/003/Math Forum/Homework 13 Part 2 (economics/demand question)</title>
		<link rel="alternate" type="text/html" href="https://wiki.ubc.ca/index.php?title=Thread:Course_talk:MATH110/003/Math_Forum/Homework_13_Part_2_(economics/demand_question)&amp;diff=75037"/>
		<updated>2011-02-03T22:20:55Z</updated>

		<summary type="html">&lt;p&gt;AdamsNguyen: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;I don&#039;t even know how to start. I spent 2 hours raging on the question... Help would be kindly appreciated.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;nowiki&amp;gt;https://chrome.google.com/webstore/img/ajjgiajaoafimgkdlcofflenackmpjhd/1292196379.87/logo128/1?itemtype=ext&lt;br /&gt;
&amp;lt;/nowiki&amp;gt;&lt;/div&gt;</summary>
		<author><name>AdamsNguyen</name></author>
	</entry>
	<entry>
		<id>https://wiki.ubc.ca/index.php?title=Thread:Course_talk:MATH110/003/Math_Forum/Homework_13_Part_2_(economics/demand_question)&amp;diff=75036</id>
		<title>Thread:Course talk:MATH110/003/Math Forum/Homework 13 Part 2 (economics/demand question)</title>
		<link rel="alternate" type="text/html" href="https://wiki.ubc.ca/index.php?title=Thread:Course_talk:MATH110/003/Math_Forum/Homework_13_Part_2_(economics/demand_question)&amp;diff=75036"/>
		<updated>2011-02-03T22:20:37Z</updated>

		<summary type="html">&lt;p&gt;AdamsNguyen: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;I don&#039;t even know how to start. I spent 2 hours raging on the question... Help would be kindly appreciated.&lt;br /&gt;
&lt;br /&gt;
[Media:https://chrome.google.com/webstore/img/ajjgiajaoafimgkdlcofflenackmpjhd/1292196379.87/logo128/1?itemtype=ext]&lt;/div&gt;</summary>
		<author><name>AdamsNguyen</name></author>
	</entry>
	<entry>
		<id>https://wiki.ubc.ca/index.php?title=Thread:Course_talk:MATH110/003/Math_Forum/Homework_13_Part_2_(economics/demand_question)&amp;diff=75035</id>
		<title>Thread:Course talk:MATH110/003/Math Forum/Homework 13 Part 2 (economics/demand question)</title>
		<link rel="alternate" type="text/html" href="https://wiki.ubc.ca/index.php?title=Thread:Course_talk:MATH110/003/Math_Forum/Homework_13_Part_2_(economics/demand_question)&amp;diff=75035"/>
		<updated>2011-02-03T22:20:24Z</updated>

		<summary type="html">&lt;p&gt;AdamsNguyen: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;I don&#039;t even know how to start. I spent 2 hours raging on the question... Help would be kindly appreciated.&lt;br /&gt;
&lt;br /&gt;
[[Media:https://chrome.google.com/webstore/img/ajjgiajaoafimgkdlcofflenackmpjhd/1292196379.87/logo128/1?itemtype=ext]]&lt;/div&gt;</summary>
		<author><name>AdamsNguyen</name></author>
	</entry>
	<entry>
		<id>https://wiki.ubc.ca/index.php?title=Thread:Course_talk:MATH110/003/Math_Forum/Homework_13_Part_2_(economics/demand_question)&amp;diff=75033</id>
		<title>Thread:Course talk:MATH110/003/Math Forum/Homework 13 Part 2 (economics/demand question)</title>
		<link rel="alternate" type="text/html" href="https://wiki.ubc.ca/index.php?title=Thread:Course_talk:MATH110/003/Math_Forum/Homework_13_Part_2_(economics/demand_question)&amp;diff=75033"/>
		<updated>2011-02-03T22:19:52Z</updated>

		<summary type="html">&lt;p&gt;AdamsNguyen: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;I don&#039;t even know how to start. I spent 2 hours raging on the question... Help would be kindly appreciated.&lt;br /&gt;
&lt;br /&gt;
[[File:https://chrome.google.com/webstore/img/ajjgiajaoafimgkdlcofflenackmpjhd/1292196379.87/logo128/1?itemtype=ext]]&lt;/div&gt;</summary>
		<author><name>AdamsNguyen</name></author>
	</entry>
	<entry>
		<id>https://wiki.ubc.ca/index.php?title=Thread:Course_talk:MATH110/003/Math_Forum/Homework_13_Part_2_(economics/demand_question)&amp;diff=75032</id>
		<title>Thread:Course talk:MATH110/003/Math Forum/Homework 13 Part 2 (economics/demand question)</title>
		<link rel="alternate" type="text/html" href="https://wiki.ubc.ca/index.php?title=Thread:Course_talk:MATH110/003/Math_Forum/Homework_13_Part_2_(economics/demand_question)&amp;diff=75032"/>
		<updated>2011-02-03T22:19:34Z</updated>

		<summary type="html">&lt;p&gt;AdamsNguyen: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;I don&#039;t even know how to start. I spent 2 hours raging on the question... Help would be kindly appreciated.&lt;br /&gt;
&lt;br /&gt;
[https://chrome.google.com/webstore/img/ajjgiajaoafimgkdlcofflenackmpjhd/1292196379.87/logo128/1?itemtype=ext]&lt;/div&gt;</summary>
		<author><name>AdamsNguyen</name></author>
	</entry>
	<entry>
		<id>https://wiki.ubc.ca/index.php?title=Thread:Course_talk:MATH110/003/Math_Forum/Homework_13_Part_2_(economics/demand_question)&amp;diff=75031</id>
		<title>Thread:Course talk:MATH110/003/Math Forum/Homework 13 Part 2 (economics/demand question)</title>
		<link rel="alternate" type="text/html" href="https://wiki.ubc.ca/index.php?title=Thread:Course_talk:MATH110/003/Math_Forum/Homework_13_Part_2_(economics/demand_question)&amp;diff=75031"/>
		<updated>2011-02-03T22:19:18Z</updated>

		<summary type="html">&lt;p&gt;AdamsNguyen: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;I don&#039;t even know how to start. I spent 2 hours raging on the question... Help would be kindly appreciated.&lt;br /&gt;
&lt;br /&gt;
https://chrome.google.com/webstore/img/ajjgiajaoafimgkdlcofflenackmpjhd/1292196379.87/logo128/1?itemtype=ext&lt;/div&gt;</summary>
		<author><name>AdamsNguyen</name></author>
	</entry>
	<entry>
		<id>https://wiki.ubc.ca/index.php?title=Thread:Course_talk:MATH110/003/Math_Forum/Homework_13_Part_2_(economics/demand_question)&amp;diff=75030</id>
		<title>Thread:Course talk:MATH110/003/Math Forum/Homework 13 Part 2 (economics/demand question)</title>
		<link rel="alternate" type="text/html" href="https://wiki.ubc.ca/index.php?title=Thread:Course_talk:MATH110/003/Math_Forum/Homework_13_Part_2_(economics/demand_question)&amp;diff=75030"/>
		<updated>2011-02-03T22:17:17Z</updated>

		<summary type="html">&lt;p&gt;AdamsNguyen: New thread: Homework 13 Part 2 (economics/demand question)&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;I don&#039;t even know how to start. I spent 2 hours raging on the question... Help would be kindly appreciated.&lt;/div&gt;</summary>
		<author><name>AdamsNguyen</name></author>
	</entry>
	<entry>
		<id>https://wiki.ubc.ca/index.php?title=User:AdamsNguyen&amp;diff=72488</id>
		<title>User:AdamsNguyen</title>
		<link rel="alternate" type="text/html" href="https://wiki.ubc.ca/index.php?title=User:AdamsNguyen&amp;diff=72488"/>
		<updated>2011-01-25T22:48:24Z</updated>

		<summary type="html">&lt;p&gt;AdamsNguyen: /* Calculus in Conservation */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;Hi There!, my name is Adam Nguyen and I am a first year Arts Student at UBC. --[[User:AdamsNguyen|AdamsNguyen]] 02:12, 18 September 2010 (UTC)&lt;br /&gt;
&lt;br /&gt;
==Essay Assignments==&lt;br /&gt;
&lt;br /&gt;
=== Calculus in Conservation ===&lt;br /&gt;
&lt;br /&gt;
Caluclus is simply defined as “the study of change”. Understanding this, one can see its vast practicability and application in all fields of careers. This “change” that one might study could be a change of price with respect to demand or the change of temperature with respect to green house gases. The possibilities are endless.&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
One particular field of interest is the environment and its conservation and sustainability. Here again, calculus is pivotal in the advancement and understanding of the environment. When considering the sustainability and the conservation for a particular ecosystem, one must be able to understand the dynamics of the organisms living within it. Most importantly, one must understand how much organisms, or more specifically, how many individuals of a given species that the ecosystem can sustain. This population limit, influenced by factors such as resource and space, is also known as the carrying capacity. Once understanding the carrying capacity of a particular environment, scientists and conservationists can effectively construct a plan for its future with minimal effects and consequences to its sustainability.&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Furthermore, we can even predict the growth rate of the population, the change in number of individuals in the population per unit time. If we can determine the carrying capacity of a habitat, the instantaneous growth rate of specie and its initial population, we can derive its growth rate.  A logistic growth equation can be formulated with all these parameters to determine a growth rate of population:&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
[[File:logisticequation1.gif]]&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
In this expression,&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
dN/dt = growth rate&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
r = instantaneous growth rate or per-capita rate of increase&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
N = the initial population&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
t = time (year)&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
K = Carrying capacity&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
(K-N)/K = the proportion of individuals that can be sustained within the carrying capacity&lt;br /&gt;
By dividing (K-N) by K, we put the individuals into a proportion that can be sustained in the environment. The carrying capacity is influenced by many factors including food, water, soil quality, space, breeding sites, predation and diseases. As we can see in this equation, if N is a small number with respect to K, the change in population per unit time, or growth rate, is relatively high. However, if N is close to the K, then (K-N)/K will be close to 0 and the growth rate will be of a lower number.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
Here is an example of the logistic growth equation in action:&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
We have a population 40 bonobo chimps in a habitat that has a carrying capacity of 450 bonobo chimps and the instantaneous growth rate of these chimps is 2.5. What is the growth rate of this population? We will use the logistic growth equation and our following function will be:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
dN/dt = (2.5)(40)((450-40)/450)&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
dN/dt = 91.1111111&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The change in the number of individuals in this population per unit time (year) is 91. This means that we would expect to see this population of bonobos to grow to 131 by the following year. This kind of key information can be very important to a researcher who wishes to rehabilitate a damaged habitat.&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
As you can see with this example in the theme of conservation, calculus plays a very important role in all kinds of careers and jobs.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===The Pythagorean Theorem===&lt;br /&gt;
&lt;br /&gt;
The Pythagorean Theorem can be simply explained through the equation: &lt;br /&gt;
&amp;lt;math&amp;gt;a^2+b^2=c^2&amp;lt;/math&amp;gt;. &lt;br /&gt;
This theory states that the squared value of the hypotenuse (the long side of a triangle) in a right triangle is equal to the sum of the squared values of the two other sides in the right triangle. With this useful knowledge, we would be able to solve many things relating to triangles! Some people would only think that the application of this theory is only contained within a classroom, but they are wrong! The application of the Pythagorean Theorem is also extensively used in real life situations as well. Here is a simple situation where one would be able to use the Pythagorean theory to resolve his or her problem. Imagine that you are at the south-western corner of a rectangular field that stretches 5 km long and 3 km wide. You have a friend that is on the north-eastern corner of this rectangular field and you want to meet her. Would it be closer to travel along the sides of this field or to travel straight through the field towards her? We can use the Pythagorean Theorem to resolve our problem! We can diagonally split this field so that we have a right triangle. The distance (d) between us and our friend on the other corner can be expressed through the equation &lt;br /&gt;
&amp;lt;math&amp;gt;d^2+3^2=5^2&amp;lt;/math&amp;gt;&lt;br /&gt;
We then use simple algebraic techniques to simplify this equation and we find that the distance (d) is only 4 km! That is twice as short of a distance compared to walking along the edge of the field. &lt;br /&gt;
Although this situation is relatively simple, if we can look at everyday life with the perspective of triangles, then the application of the Pythagorean Theorem in real life is limitless!&lt;br /&gt;
&lt;br /&gt;
Mueller, Guntram, and Ronald I. Brent. Just-in-time: Algebra and Trigonometry for Calculus. Boston: Pearson/Addison-Wesley, 2005. Print.&lt;br /&gt;
&lt;br /&gt;
Katz, Victor J. A History of Mathematics. New York, New York: Harper Collin, 1993.&lt;/div&gt;</summary>
		<author><name>AdamsNguyen</name></author>
	</entry>
	<entry>
		<id>https://wiki.ubc.ca/index.php?title=User:AdamsNguyen&amp;diff=72484</id>
		<title>User:AdamsNguyen</title>
		<link rel="alternate" type="text/html" href="https://wiki.ubc.ca/index.php?title=User:AdamsNguyen&amp;diff=72484"/>
		<updated>2011-01-25T22:47:50Z</updated>

		<summary type="html">&lt;p&gt;AdamsNguyen: /* Calculus in Conservation */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;Hi There!, my name is Adam Nguyen and I am a first year Arts Student at UBC. --[[User:AdamsNguyen|AdamsNguyen]] 02:12, 18 September 2010 (UTC)&lt;br /&gt;
&lt;br /&gt;
==Essay Assignments==&lt;br /&gt;
&lt;br /&gt;
=== Calculus in Conservation ===&lt;br /&gt;
&lt;br /&gt;
Caluclus is simply defined as “the study of change”. Understanding this, one can see its vast practicability and application in all fields of science and jobs. This “change” that one might study could be a change of price with respect to demand or the change of temperature with respect to green house gases. The possibilities are endless.&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
One particular field of interest is the environment and its conservation and sustainability. Here again, calculus is pivotal in the advancement and understanding of the environment. When considering the sustainability and the conservation for a particular ecosystem, one must be able to understand the dynamics of the organisms living within it. Most importantly, one must understand how much organisms, or more specifically, how many individuals of a given species that the ecosystem can sustain. This population limit, influenced by factors such as resource and space, is also known as the carrying capacity. Once understanding the carrying capacity of a particular environment, scientists and conservationists can effectively construct a plan for its future with minimal effects and consequences to its sustainability.&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Furthermore, we can even predict the growth rate of the population, the change in number of individuals in the population per unit time. If we can determine the carrying capacity of a habitat, the instantaneous growth rate of specie and its initial population, we can derive its growth rate.  A logistic growth equation can be formulated with all these parameters to determine a growth rate of population:&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
[[File:logisticequation1.gif]]&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
In this expression,&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
dN/dt = growth rate&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
r = instantaneous growth rate or per-capita rate of increase&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
N = the initial population&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
t = time (year)&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
K = Carrying capacity&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
(K-N)/K = the proportion of individuals that can be sustained within the carrying capacity&lt;br /&gt;
By dividing (K-N) by K, we put the individuals into a proportion that can be sustained in the environment. The carrying capacity is influenced by many factors including food, water, soil quality, space, breeding sites, predation and diseases. As we can see in this equation, if N is a small number with respect to K, the change in population per unit time, or growth rate, is relatively high. However, if N is close to the K, then (K-N)/K will be close to 0 and the growth rate will be of a lower number.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
Here is an example of the logistic growth equation in action:&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
We have a population 40 bonobo chimps in a habitat that has a carrying capacity of 450 bonobo chimps and the instantaneous growth rate of these chimps is 2.5. What is the growth rate of this population? We will use the logistic growth equation and our following function will be:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
dN/dt = (2.5)(40)((450-40)/450)&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
dN/dt = 91.1111111&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The change in the number of individuals in this population per unit time (year) is 91. This means that we would expect to see this population of bonobos to grow to 131 by the following year. This kind of key information can be very important to a researcher who wishes to rehabilitate a damaged habitat.&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
As you can see with this example in the theme of conservation, calculus plays a very important role in all kinds of careers and jobs.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===The Pythagorean Theorem===&lt;br /&gt;
&lt;br /&gt;
The Pythagorean Theorem can be simply explained through the equation: &lt;br /&gt;
&amp;lt;math&amp;gt;a^2+b^2=c^2&amp;lt;/math&amp;gt;. &lt;br /&gt;
This theory states that the squared value of the hypotenuse (the long side of a triangle) in a right triangle is equal to the sum of the squared values of the two other sides in the right triangle. With this useful knowledge, we would be able to solve many things relating to triangles! Some people would only think that the application of this theory is only contained within a classroom, but they are wrong! The application of the Pythagorean Theorem is also extensively used in real life situations as well. Here is a simple situation where one would be able to use the Pythagorean theory to resolve his or her problem. Imagine that you are at the south-western corner of a rectangular field that stretches 5 km long and 3 km wide. You have a friend that is on the north-eastern corner of this rectangular field and you want to meet her. Would it be closer to travel along the sides of this field or to travel straight through the field towards her? We can use the Pythagorean Theorem to resolve our problem! We can diagonally split this field so that we have a right triangle. The distance (d) between us and our friend on the other corner can be expressed through the equation &lt;br /&gt;
&amp;lt;math&amp;gt;d^2+3^2=5^2&amp;lt;/math&amp;gt;&lt;br /&gt;
We then use simple algebraic techniques to simplify this equation and we find that the distance (d) is only 4 km! That is twice as short of a distance compared to walking along the edge of the field. &lt;br /&gt;
Although this situation is relatively simple, if we can look at everyday life with the perspective of triangles, then the application of the Pythagorean Theorem in real life is limitless!&lt;br /&gt;
&lt;br /&gt;
Mueller, Guntram, and Ronald I. Brent. Just-in-time: Algebra and Trigonometry for Calculus. Boston: Pearson/Addison-Wesley, 2005. Print.&lt;br /&gt;
&lt;br /&gt;
Katz, Victor J. A History of Mathematics. New York, New York: Harper Collin, 1993.&lt;/div&gt;</summary>
		<author><name>AdamsNguyen</name></author>
	</entry>
	<entry>
		<id>https://wiki.ubc.ca/index.php?title=User:AdamsNguyen&amp;diff=72482</id>
		<title>User:AdamsNguyen</title>
		<link rel="alternate" type="text/html" href="https://wiki.ubc.ca/index.php?title=User:AdamsNguyen&amp;diff=72482"/>
		<updated>2011-01-25T22:47:31Z</updated>

		<summary type="html">&lt;p&gt;AdamsNguyen: /* Calculus in Conservation */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;Hi There!, my name is Adam Nguyen and I am a first year Arts Student at UBC. --[[User:AdamsNguyen|AdamsNguyen]] 02:12, 18 September 2010 (UTC)&lt;br /&gt;
&lt;br /&gt;
==Essay Assignments==&lt;br /&gt;
&lt;br /&gt;
=== Calculus in Conservation ===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
Caluclus is simply defined as “the study of change”. Understanding this, one can see its vast practicability and application in all fields of science and jobs. This “change” that one might study could be a change of price with respect to demand or the change of temperature with respect to green house gases. The possibilities are endless.&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
One particular field of interest is the environment and its conservation and sustainability. Here again, calculus is pivotal in the advancement and understanding of the environment. When considering the sustainability and the conservation for a particular ecosystem, one must be able to understand the dynamics of the organisms living within it. Most importantly, one must understand how much organisms, or more specifically, how many individuals of a given species that the ecosystem can sustain. This population limit, influenced by factors such as resource and space, is also known as the carrying capacity. Once understanding the carrying capacity of a particular environment, scientists and conservationists can effectively construct a plan for its future with minimal effects and consequences to its sustainability.&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Furthermore, we can even predict the growth rate of the population, the change in number of individuals in the population per unit time. If we can determine the carrying capacity of a habitat, the instantaneous growth rate of specie and its initial population, we can derive its growth rate.  A logistic growth equation can be formulated with all these parameters to determine a growth rate of population:&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
[[File:logisticequation1.gif]]&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
In this expression,&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
dN/dt = growth rate&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
r = instantaneous growth rate or per-capita rate of increase&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
N = the initial population&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
t = time (year)&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
K = Carrying capacity&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
(K-N)/K = the proportion of individuals that can be sustained within the carrying capacity&lt;br /&gt;
By dividing (K-N) by K, we put the individuals into a proportion that can be sustained in the environment. The carrying capacity is influenced by many factors including food, water, soil quality, space, breeding sites, predation and diseases. As we can see in this equation, if N is a small number with respect to K, the change in population per unit time, or growth rate, is relatively high. However, if N is close to the K, then (K-N)/K will be close to 0 and the growth rate will be of a lower number.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
Here is an example of the logistic growth equation in action:&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
We have a population 40 bonobo chimps in a habitat that has a carrying capacity of 450 bonobo chimps and the instantaneous growth rate of these chimps is 2.5. What is the growth rate of this population? We will use the logistic growth equation and our following function will be:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
dN/dt = (2.5)(40)((450-40)/450)&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
dN/dt = 91.1111111&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The change in the number of individuals in this population per unit time (year) is 91. This means that we would expect to see this population of bonobos to grow to 131 by the following year. This kind of key information can be very important to a researcher who wishes to rehabilitate a damaged habitat.&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
As you can see with this example in the theme of conservation, calculus plays a very important role in all kinds of careers and jobs.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===The Pythagorean Theorem===&lt;br /&gt;
&lt;br /&gt;
The Pythagorean Theorem can be simply explained through the equation: &lt;br /&gt;
&amp;lt;math&amp;gt;a^2+b^2=c^2&amp;lt;/math&amp;gt;. &lt;br /&gt;
This theory states that the squared value of the hypotenuse (the long side of a triangle) in a right triangle is equal to the sum of the squared values of the two other sides in the right triangle. With this useful knowledge, we would be able to solve many things relating to triangles! Some people would only think that the application of this theory is only contained within a classroom, but they are wrong! The application of the Pythagorean Theorem is also extensively used in real life situations as well. Here is a simple situation where one would be able to use the Pythagorean theory to resolve his or her problem. Imagine that you are at the south-western corner of a rectangular field that stretches 5 km long and 3 km wide. You have a friend that is on the north-eastern corner of this rectangular field and you want to meet her. Would it be closer to travel along the sides of this field or to travel straight through the field towards her? We can use the Pythagorean Theorem to resolve our problem! We can diagonally split this field so that we have a right triangle. The distance (d) between us and our friend on the other corner can be expressed through the equation &lt;br /&gt;
&amp;lt;math&amp;gt;d^2+3^2=5^2&amp;lt;/math&amp;gt;&lt;br /&gt;
We then use simple algebraic techniques to simplify this equation and we find that the distance (d) is only 4 km! That is twice as short of a distance compared to walking along the edge of the field. &lt;br /&gt;
Although this situation is relatively simple, if we can look at everyday life with the perspective of triangles, then the application of the Pythagorean Theorem in real life is limitless!&lt;br /&gt;
&lt;br /&gt;
Mueller, Guntram, and Ronald I. Brent. Just-in-time: Algebra and Trigonometry for Calculus. Boston: Pearson/Addison-Wesley, 2005. Print.&lt;br /&gt;
&lt;br /&gt;
Katz, Victor J. A History of Mathematics. New York, New York: Harper Collin, 1993.&lt;/div&gt;</summary>
		<author><name>AdamsNguyen</name></author>
	</entry>
	<entry>
		<id>https://wiki.ubc.ca/index.php?title=User:AdamsNguyen&amp;diff=72478</id>
		<title>User:AdamsNguyen</title>
		<link rel="alternate" type="text/html" href="https://wiki.ubc.ca/index.php?title=User:AdamsNguyen&amp;diff=72478"/>
		<updated>2011-01-25T22:46:45Z</updated>

		<summary type="html">&lt;p&gt;AdamsNguyen: /* Calculus in Conservation */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;Hi There!, my name is Adam Nguyen and I am a first year Arts Student at UBC. --[[User:AdamsNguyen|AdamsNguyen]] 02:12, 18 September 2010 (UTC)&lt;br /&gt;
&lt;br /&gt;
==Essay Assignments==&lt;br /&gt;
&lt;br /&gt;
=== Calculus in Conservation ===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
Caluclus is simply defined as “the study of change”. Understanding this, one can see its vast practicability and application in all fields of science and jobs. This “change” that one might study could be a change of price with respect to demand or the change of temperature with respect to green house gases. The possibilities are endless.&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
One particular field of interest is the environment and its conservation and sustainability. Here again, calculus is pivotal in the advancement and understanding of the environment. When considering the sustainability and the conservation for a particular ecosystem, one must be able to understand the dynamics of the organisms living within it. Most importantly, one must understand how much organisms, or more specifically, how many individuals of a given species that the ecosystem can sustain. This population limit, influenced by factors such as resource and space, is also known as the carrying capacity. Once understanding the carrying capacity of a particular environment, scientists and conservationists can effectively construct a plan for its future with minimal effects and consequences to its sustainability.&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
Furthermore, we can even predict the growth rate of the population, the change in number of individuals in the population per unit time. If we can determine the carrying capacity of a habitat, the instantaneous growth rate of specie and its initial population, we can derive its growth rate.  A logistic growth equation can be formulated with all these parameters to determine a growth rate of population:&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
[[File:logisticequation1.gif]]&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
In this expression,&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
dN/dt = growth rate&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
r = instantaneous growth rate or per-capita rate of increase&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
N = the initial population&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
t = time (year)&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
K = Carrying capacity&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
(K-N)/K = the proportion of individuals that can be sustained within the carrying capacity&lt;br /&gt;
By dividing (K-N) by K, we put the individuals into a proportion that can be sustained in the environment. The carrying capacity is influenced by many factors including food, water, soil quality, space, breeding sites, predation and diseases. As we can see in this equation, if N is a small number with respect to K, the change in population per unit time, or growth rate, is relatively high. However, if N is close to the K, then (K-N)/K will be close to 0 and the growth rate will be of a lower number.&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
Here is an example of the logistic growth equation in action:&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
We have a population 40 bonobo chimps in a habitat that has a carrying capacity of 450 bonobo chimps and the instantaneous growth rate of these chimps is 2.5. What is the growth rate of this population? We will use the logistic growth equation and our following function will be:&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
dN/dt = (2.5)(40)((450-40)/450)&lt;br /&gt;
dN/dt = 91.1111111&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The change in the number of individuals in this population per unit time (year) is 91. This means that we would expect to see this population of bonobos to grow to 131 by the following year. This kind of key information can be very important to a researcher who wishes to rehabilitate a damaged habitat.&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
As you can see with this example in the theme of conservation, calculus plays a very important role in all kinds of careers and jobs.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===The Pythagorean Theorem===&lt;br /&gt;
&lt;br /&gt;
The Pythagorean Theorem can be simply explained through the equation: &lt;br /&gt;
&amp;lt;math&amp;gt;a^2+b^2=c^2&amp;lt;/math&amp;gt;. &lt;br /&gt;
This theory states that the squared value of the hypotenuse (the long side of a triangle) in a right triangle is equal to the sum of the squared values of the two other sides in the right triangle. With this useful knowledge, we would be able to solve many things relating to triangles! Some people would only think that the application of this theory is only contained within a classroom, but they are wrong! The application of the Pythagorean Theorem is also extensively used in real life situations as well. Here is a simple situation where one would be able to use the Pythagorean theory to resolve his or her problem. Imagine that you are at the south-western corner of a rectangular field that stretches 5 km long and 3 km wide. You have a friend that is on the north-eastern corner of this rectangular field and you want to meet her. Would it be closer to travel along the sides of this field or to travel straight through the field towards her? We can use the Pythagorean Theorem to resolve our problem! We can diagonally split this field so that we have a right triangle. The distance (d) between us and our friend on the other corner can be expressed through the equation &lt;br /&gt;
&amp;lt;math&amp;gt;d^2+3^2=5^2&amp;lt;/math&amp;gt;&lt;br /&gt;
We then use simple algebraic techniques to simplify this equation and we find that the distance (d) is only 4 km! That is twice as short of a distance compared to walking along the edge of the field. &lt;br /&gt;
Although this situation is relatively simple, if we can look at everyday life with the perspective of triangles, then the application of the Pythagorean Theorem in real life is limitless!&lt;br /&gt;
&lt;br /&gt;
Mueller, Guntram, and Ronald I. Brent. Just-in-time: Algebra and Trigonometry for Calculus. Boston: Pearson/Addison-Wesley, 2005. Print.&lt;br /&gt;
&lt;br /&gt;
Katz, Victor J. A History of Mathematics. New York, New York: Harper Collin, 1993.&lt;/div&gt;</summary>
		<author><name>AdamsNguyen</name></author>
	</entry>
	<entry>
		<id>https://wiki.ubc.ca/index.php?title=User:AdamsNguyen&amp;diff=72471</id>
		<title>User:AdamsNguyen</title>
		<link rel="alternate" type="text/html" href="https://wiki.ubc.ca/index.php?title=User:AdamsNguyen&amp;diff=72471"/>
		<updated>2011-01-25T22:45:45Z</updated>

		<summary type="html">&lt;p&gt;AdamsNguyen: /* Calculus in Conservation */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;Hi There!, my name is Adam Nguyen and I am a first year Arts Student at UBC. --[[User:AdamsNguyen|AdamsNguyen]] 02:12, 18 September 2010 (UTC)&lt;br /&gt;
&lt;br /&gt;
==Essay Assignments==&lt;br /&gt;
&lt;br /&gt;
=== Calculus in Conservation ===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
Caluclus is simply defined as “the study of change”. Understanding this, one can see its vast practicability and application in all fields of science and jobs. This “change” that one might study could be a change of price with respect to demand or the change of temperature with respect to green house gases. The possibilities are endless.&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
One particular field of interest is the environment and its conservation and sustainability. Here again, calculus is pivotal in the advancement and understanding of the environment. When considering the sustainability and the conservation for a particular ecosystem, one must be able to understand the dynamics of the organisms living within it. Most importantly, one must understand how much organisms, or more specifically, how many individuals of a given species that the ecosystem can sustain. This population limit, influenced by factors such as resource and space, is also known as the carrying capacity. Once understanding the carrying capacity of a particular environment, scientists and conservationists can effectively construct a plan for its future with minimal effects and consequences to its sustainability.&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
Furthermore, we can even predict the growth rate of the population, the change in number of individuals in the population per unit time. If we can determine the carrying capacity of a habitat, the instantaneous growth rate of specie and its initial population, we can derive its growth rate.  A logistic growth equation can be formulated with all these parameters to determine a growth rate of population:&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
[[File:logisticequation1.gif]]&lt;br /&gt;
In this expression,&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
dN/dt = growth rate&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
r = instantaneous growth rate or per-capita rate of increase&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
N = the initial population&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
t = time (year)&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
K = Carrying capacity&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
(K-N)/K = the proportion of individuals that can be sustained within the carrying capacity&lt;br /&gt;
By dividing (K-N) by K, we put the individuals into a proportion that can be sustained in the environment. The carrying capacity is influenced by many factors including food, water, soil quality, space, breeding sites, predation and diseases. As we can see in this equation, if N is a small number with respect to K, the change in population per unit time, or growth rate, is relatively high. However, if N is close to the K, then (K-N)/K will be close to 0 and the growth rate will be of a lower number.&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
Here is an example of the logistic growth equation in action:&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
We have a population 40 bonobo chimps in a habitat that has a carrying capacity of 450 bonobo chimps and the instantaneous growth rate of these chimps is 2.5. What is the growth rate of this population? We will use the logistic growth equation and our following function will be:&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
dN/dt = (2.5)(40)((450-40)/450)&lt;br /&gt;
dN/dt = 91.1111111&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
The change in the number of individuals in this population per unit time (year) is 91. This means that we would expect to see this population of bonobos to grow to 131 by the following year. This kind of key information can be very important to a researcher who wishes to rehabilitate a damaged habitat.&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
As you can see with this example in the theme of conservation, calculus plays a very important role in all kinds of careers and jobs.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===The Pythagorean Theorem===&lt;br /&gt;
&lt;br /&gt;
The Pythagorean Theorem can be simply explained through the equation: &lt;br /&gt;
&amp;lt;math&amp;gt;a^2+b^2=c^2&amp;lt;/math&amp;gt;. &lt;br /&gt;
This theory states that the squared value of the hypotenuse (the long side of a triangle) in a right triangle is equal to the sum of the squared values of the two other sides in the right triangle. With this useful knowledge, we would be able to solve many things relating to triangles! Some people would only think that the application of this theory is only contained within a classroom, but they are wrong! The application of the Pythagorean Theorem is also extensively used in real life situations as well. Here is a simple situation where one would be able to use the Pythagorean theory to resolve his or her problem. Imagine that you are at the south-western corner of a rectangular field that stretches 5 km long and 3 km wide. You have a friend that is on the north-eastern corner of this rectangular field and you want to meet her. Would it be closer to travel along the sides of this field or to travel straight through the field towards her? We can use the Pythagorean Theorem to resolve our problem! We can diagonally split this field so that we have a right triangle. The distance (d) between us and our friend on the other corner can be expressed through the equation &lt;br /&gt;
&amp;lt;math&amp;gt;d^2+3^2=5^2&amp;lt;/math&amp;gt;&lt;br /&gt;
We then use simple algebraic techniques to simplify this equation and we find that the distance (d) is only 4 km! That is twice as short of a distance compared to walking along the edge of the field. &lt;br /&gt;
Although this situation is relatively simple, if we can look at everyday life with the perspective of triangles, then the application of the Pythagorean Theorem in real life is limitless!&lt;br /&gt;
&lt;br /&gt;
Mueller, Guntram, and Ronald I. Brent. Just-in-time: Algebra and Trigonometry for Calculus. Boston: Pearson/Addison-Wesley, 2005. Print.&lt;br /&gt;
&lt;br /&gt;
Katz, Victor J. A History of Mathematics. New York, New York: Harper Collin, 1993.&lt;/div&gt;</summary>
		<author><name>AdamsNguyen</name></author>
	</entry>
	<entry>
		<id>https://wiki.ubc.ca/index.php?title=User:AdamsNguyen&amp;diff=72458</id>
		<title>User:AdamsNguyen</title>
		<link rel="alternate" type="text/html" href="https://wiki.ubc.ca/index.php?title=User:AdamsNguyen&amp;diff=72458"/>
		<updated>2011-01-25T22:44:15Z</updated>

		<summary type="html">&lt;p&gt;AdamsNguyen: /* Calculus in Conservation */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;Hi There!, my name is Adam Nguyen and I am a first year Arts Student at UBC. --[[User:AdamsNguyen|AdamsNguyen]] 02:12, 18 September 2010 (UTC)&lt;br /&gt;
&lt;br /&gt;
==Essay Assignments==&lt;br /&gt;
&lt;br /&gt;
=== Calculus in Conservation ===&lt;br /&gt;
&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Caluclus is simply defined as “the study of change”. Understanding this, one can see its vast practicability and application in all fields of science and jobs. This “change” that one might study could be a change of price with respect to demand or the change of temperature with respect to green house gases. The possibilities are endless.&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
 One particular field of interest is the environment and its conservation and sustainability. Here again, calculus is pivotal in the advancement and understanding of the environment. When considering the sustainability and the conservation for a particular ecosystem, one must be able to understand the dynamics of the organisms living within it. Most importantly, one must understand how much organisms, or more specifically, how many individuals of a given species that the ecosystem can sustain. This population limit, influenced by factors such as resource and space, is also known as the carrying capacity. Once understanding the carrying capacity of a particular environment, scientists and conservationists can effectively construct a plan for its future with minimal effects and consequences to its sustainability.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
Furthermore, we can even predict the growth rate of the population, the change in number of individuals in the population per unit time. If we can determine the carrying capacity of a habitat, the instantaneous growth rate of specie and its initial population, we can derive its growth rate.  A logistic growth equation can be formulated with all these parameters to determine a growth rate of population:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
[[File:logisticequation1.gif]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
In this expression,&lt;br /&gt;
&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
dN/dt = growth rate&lt;br /&gt;
&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
r = instantaneous growth rate or per-capita rate of increase&lt;br /&gt;
&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
N = the initial population&lt;br /&gt;
&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
t = time (year)&lt;br /&gt;
&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
K = Carrying capacity&lt;br /&gt;
&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
(K-N)/K = the proportion of individuals that can be sustained within the carrying capacity&lt;br /&gt;
By dividing (K-N) by K, we put the individuals into a proportion that can be sustained in the environment. The carrying capacity is influenced by many factors including food, water, soil quality, space, breeding sites, predation and diseases. As we can see in this equation, if N is a small number with respect to K, the change in population per unit time, or growth rate, is relatively high. However, if N is close to the K, then (K-N)/K will be close to 0 and the growth rate will be of a lower number.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
Here is an example of the logistic growth equation in action:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
We have a population 40 bonobo chimps in a habitat that has a carrying capacity of 450 bonobo chimps and the instantaneous growth rate of these chimps is 2.5. What is the growth rate of this population? We will use the logistic growth equation and our following function will be:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
dN/dt = (2.5)(40)((450-40)/450)&lt;br /&gt;
dN/dt = 91.1111111&lt;br /&gt;
&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
The change in the number of individuals in this population per unit time (year) is 91. This means that we would expect to see this population of bonobos to grow to 131 by the following year. This kind of key information can be very important to a researcher who wishes to rehabilitate a damaged habitat.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
As you can see with this example in the theme of conservation, calculus plays a very important role in all kinds of careers and jobs.&lt;br /&gt;
&lt;br /&gt;
===The Pythagorean Theorem===&lt;br /&gt;
&lt;br /&gt;
The Pythagorean Theorem can be simply explained through the equation: &lt;br /&gt;
&amp;lt;math&amp;gt;a^2+b^2=c^2&amp;lt;/math&amp;gt;. &lt;br /&gt;
This theory states that the squared value of the hypotenuse (the long side of a triangle) in a right triangle is equal to the sum of the squared values of the two other sides in the right triangle. With this useful knowledge, we would be able to solve many things relating to triangles! Some people would only think that the application of this theory is only contained within a classroom, but they are wrong! The application of the Pythagorean Theorem is also extensively used in real life situations as well. Here is a simple situation where one would be able to use the Pythagorean theory to resolve his or her problem. Imagine that you are at the south-western corner of a rectangular field that stretches 5 km long and 3 km wide. You have a friend that is on the north-eastern corner of this rectangular field and you want to meet her. Would it be closer to travel along the sides of this field or to travel straight through the field towards her? We can use the Pythagorean Theorem to resolve our problem! We can diagonally split this field so that we have a right triangle. The distance (d) between us and our friend on the other corner can be expressed through the equation &lt;br /&gt;
&amp;lt;math&amp;gt;d^2+3^2=5^2&amp;lt;/math&amp;gt;&lt;br /&gt;
We then use simple algebraic techniques to simplify this equation and we find that the distance (d) is only 4 km! That is twice as short of a distance compared to walking along the edge of the field. &lt;br /&gt;
Although this situation is relatively simple, if we can look at everyday life with the perspective of triangles, then the application of the Pythagorean Theorem in real life is limitless!&lt;br /&gt;
&lt;br /&gt;
Mueller, Guntram, and Ronald I. Brent. Just-in-time: Algebra and Trigonometry for Calculus. Boston: Pearson/Addison-Wesley, 2005. Print.&lt;br /&gt;
&lt;br /&gt;
Katz, Victor J. A History of Mathematics. New York, New York: Harper Collin, 1993.&lt;/div&gt;</summary>
		<author><name>AdamsNguyen</name></author>
	</entry>
	<entry>
		<id>https://wiki.ubc.ca/index.php?title=File:Logisticequation1.gif&amp;diff=72447</id>
		<title>File:Logisticequation1.gif</title>
		<link rel="alternate" type="text/html" href="https://wiki.ubc.ca/index.php?title=File:Logisticequation1.gif&amp;diff=72447"/>
		<updated>2011-01-25T22:42:37Z</updated>

		<summary type="html">&lt;p&gt;AdamsNguyen: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;&lt;/div&gt;</summary>
		<author><name>AdamsNguyen</name></author>
	</entry>
	<entry>
		<id>https://wiki.ubc.ca/index.php?title=User:AdamsNguyen&amp;diff=72441</id>
		<title>User:AdamsNguyen</title>
		<link rel="alternate" type="text/html" href="https://wiki.ubc.ca/index.php?title=User:AdamsNguyen&amp;diff=72441"/>
		<updated>2011-01-25T22:42:05Z</updated>

		<summary type="html">&lt;p&gt;AdamsNguyen: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;Hi There!, my name is Adam Nguyen and I am a first year Arts Student at UBC. --[[User:AdamsNguyen|AdamsNguyen]] 02:12, 18 September 2010 (UTC)&lt;br /&gt;
&lt;br /&gt;
==Essay Assignments==&lt;br /&gt;
&lt;br /&gt;
=== Calculus in Conservation ===&lt;br /&gt;
&lt;br /&gt;
Caluclus is simply defined as “the study of change”. Understanding this, one can see its vast practicability and application in all fields of science and jobs. This “change” that one might study could be a change of price with respect to demand or the change of temperature with respect to green house gases. The possibilities are endless.&lt;br /&gt;
 One particular field of interest is the environment and its conservation and sustainability. Here again, calculus is pivotal in the advancement and understanding of the environment. When considering the sustainability and the conservation for a particular ecosystem, one must be able to understand the dynamics of the organisms living within it. Most importantly, one must understand how much organisms, or more specifically, how many individuals of a given species that the ecosystem can sustain. This population limit, influenced by factors such as resource and space, is also known as the carrying capacity. Once understanding the carrying capacity of a particular environment, scientists and conservationists can effectively construct a plan for its future with minimal effects and consequences to its sustainability.&lt;br /&gt;
Furthermore, we can even predict the growth rate of the population, the change in number of individuals in the population per unit time. If we can determine the carrying capacity of a habitat, the instantaneous growth rate of specie and its initial population, we can derive its growth rate.  A logistic growth equation can be formulated with all these parameters to determine a growth rate of population:&lt;br /&gt;
[[File:logisticequation1.gif]]&lt;br /&gt;
In this expression,&lt;br /&gt;
dN/dt = growth rate&lt;br /&gt;
r = instantaneous growth rate or per-capita rate of increase&lt;br /&gt;
N = the initial population&lt;br /&gt;
t = time (year)&lt;br /&gt;
K = Carrying capacity&lt;br /&gt;
(K-N)/K = the proportion of individuals that can be sustained within the carrying capacity&lt;br /&gt;
By dividing (K-N) by K, we put the individuals into a proportion that can be sustained in the environment. The carrying capacity is influenced by many factors including food, water, soil quality, space, breeding sites, predation and diseases. As we can see in this equation, if N is a small number with respect to K, the change in population per unit time, or growth rate, is relatively high. However, if N is close to the K, then (K-N)/K will be close to 0 and the growth rate will be of a lower number.&lt;br /&gt;
Here is an example of the logistic growth equation:&lt;br /&gt;
We have a population 40 bonobo chimps in a habitat that has a carrying capacity of 450 bonobo chimps and the instantaneous growth rate of these chimps is 2.5. What is the growth rate of this population? We will use the logistic growth equation and our following function will be:&lt;br /&gt;
dN/dt = (2.5)(40)((450-40)/450)&lt;br /&gt;
dN/dt = 91.1111111&lt;br /&gt;
The change in the number of individuals in this population per unit time (year) is 91. This means that we would expect to see this population of bonobos to grow to 131 by the following year. This kind of key information can be very important to a researcher who wishes to rehabilitate a damaged habitat.&lt;br /&gt;
As you can see with this example in the theme of conservation, calculus plays a very important role in all kinds of careers and jobs. &lt;br /&gt;
&lt;br /&gt;
===The Pythagorean Theorem===&lt;br /&gt;
&lt;br /&gt;
The Pythagorean Theorem can be simply explained through the equation: &lt;br /&gt;
&amp;lt;math&amp;gt;a^2+b^2=c^2&amp;lt;/math&amp;gt;. &lt;br /&gt;
This theory states that the squared value of the hypotenuse (the long side of a triangle) in a right triangle is equal to the sum of the squared values of the two other sides in the right triangle. With this useful knowledge, we would be able to solve many things relating to triangles! Some people would only think that the application of this theory is only contained within a classroom, but they are wrong! The application of the Pythagorean Theorem is also extensively used in real life situations as well. Here is a simple situation where one would be able to use the Pythagorean theory to resolve his or her problem. Imagine that you are at the south-western corner of a rectangular field that stretches 5 km long and 3 km wide. You have a friend that is on the north-eastern corner of this rectangular field and you want to meet her. Would it be closer to travel along the sides of this field or to travel straight through the field towards her? We can use the Pythagorean Theorem to resolve our problem! We can diagonally split this field so that we have a right triangle. The distance (d) between us and our friend on the other corner can be expressed through the equation &lt;br /&gt;
&amp;lt;math&amp;gt;d^2+3^2=5^2&amp;lt;/math&amp;gt;&lt;br /&gt;
We then use simple algebraic techniques to simplify this equation and we find that the distance (d) is only 4 km! That is twice as short of a distance compared to walking along the edge of the field. &lt;br /&gt;
Although this situation is relatively simple, if we can look at everyday life with the perspective of triangles, then the application of the Pythagorean Theorem in real life is limitless!&lt;br /&gt;
&lt;br /&gt;
Mueller, Guntram, and Ronald I. Brent. Just-in-time: Algebra and Trigonometry for Calculus. Boston: Pearson/Addison-Wesley, 2005. Print.&lt;br /&gt;
&lt;br /&gt;
Katz, Victor J. A History of Mathematics. New York, New York: Harper Collin, 1993.&lt;/div&gt;</summary>
		<author><name>AdamsNguyen</name></author>
	</entry>
	<entry>
		<id>https://wiki.ubc.ca/index.php?title=Course:MATH110/Archive/2010-2011/003/Teams/Jura&amp;diff=71813</id>
		<title>Course:MATH110/Archive/2010-2011/003/Teams/Jura</title>
		<link rel="alternate" type="text/html" href="https://wiki.ubc.ca/index.php?title=Course:MATH110/Archive/2010-2011/003/Teams/Jura&amp;diff=71813"/>
		<updated>2011-01-24T16:11:56Z</updated>

		<summary type="html">&lt;p&gt;AdamsNguyen: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;{{Infobox MATH110 Teams&lt;br /&gt;
| team name = Jura&lt;br /&gt;
| member 1 = [mailto:adam@premierwestmma.com Adam Nguyen] - Grapple&lt;br /&gt;
| member 2 = Christa Bicego - Achieve&lt;br /&gt;
| member 3 = [mailto:matthew.hsu@gmail.com Matthew Hsu]&lt;br /&gt;
| member 4 = Shamilla Birring - Effort&lt;br /&gt;
}}&lt;br /&gt;
&lt;br /&gt;
==discussion==&lt;br /&gt;
&lt;br /&gt;
Hey guys, I&#039;ve been playing with the &lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
(1/(1+e^-t)) &lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
function and I came to a few conclusions&lt;br /&gt;
&lt;br /&gt;
I was able to modify the function with a few added variables. The new functions becomes:&amp;lt;br&amp;gt;&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
(1(q))/(1+we^(-rt)).&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
q - will determine the horizontal asymptote on the right&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
w - will determine at what y should be when t (or x) is 0&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
r - will determine how quickly or slowly the growth will be.&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
Take a look!&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
- Adam&lt;br /&gt;
&lt;br /&gt;
== Workshop ==&lt;br /&gt;
In workshop L.&lt;br /&gt;
&lt;br /&gt;
== Homework ==&lt;br /&gt;
http://wiki.ubc.ca/Course:MATH110/003/Teams/Jura/Homework/&lt;/div&gt;</summary>
		<author><name>AdamsNguyen</name></author>
	</entry>
	<entry>
		<id>https://wiki.ubc.ca/index.php?title=Course:MATH110/Archive/2010-2011/003/Teams/Jura&amp;diff=71808</id>
		<title>Course:MATH110/Archive/2010-2011/003/Teams/Jura</title>
		<link rel="alternate" type="text/html" href="https://wiki.ubc.ca/index.php?title=Course:MATH110/Archive/2010-2011/003/Teams/Jura&amp;diff=71808"/>
		<updated>2011-01-24T16:11:30Z</updated>

		<summary type="html">&lt;p&gt;AdamsNguyen: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;{{Infobox MATH110 Teams&lt;br /&gt;
| team name = Jura&lt;br /&gt;
| member 1 = [mailto:adam@premierwestmma.com Adam Nguyen] - Grapple&lt;br /&gt;
| member 2 = Christa Bicego - Achieve&lt;br /&gt;
| member 3 = [mailto:matthew.hsu@gmail.com Matthew Hsu]&lt;br /&gt;
| member 4 = Shamilla Birring - Success&lt;br /&gt;
}}&lt;br /&gt;
&lt;br /&gt;
==discussion==&lt;br /&gt;
&lt;br /&gt;
Hey guys, I&#039;ve been playing with the &lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
(1/(1+e^-t)) &lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
function and I came to a few conclusions&lt;br /&gt;
&lt;br /&gt;
I was able to modify the function with a few added variables. The new functions becomes:&amp;lt;br&amp;gt;&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
(1(q))/(1+we^(-rt)).&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
q - will determine the horizontal asymptote on the right&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
w - will determine at what y should be when t (or x) is 0&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
r - will determine how quickly or slowly the growth will be.&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
Take a look!&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
- Adam&lt;br /&gt;
&lt;br /&gt;
== Workshop ==&lt;br /&gt;
In workshop L.&lt;br /&gt;
&lt;br /&gt;
== Homework ==&lt;br /&gt;
http://wiki.ubc.ca/Course:MATH110/003/Teams/Jura/Homework/&lt;/div&gt;</summary>
		<author><name>AdamsNguyen</name></author>
	</entry>
	<entry>
		<id>https://wiki.ubc.ca/index.php?title=Course:MATH110/Archive/2010-2011/003/Teams/Jura&amp;diff=71769</id>
		<title>Course:MATH110/Archive/2010-2011/003/Teams/Jura</title>
		<link rel="alternate" type="text/html" href="https://wiki.ubc.ca/index.php?title=Course:MATH110/Archive/2010-2011/003/Teams/Jura&amp;diff=71769"/>
		<updated>2011-01-24T03:13:58Z</updated>

		<summary type="html">&lt;p&gt;AdamsNguyen: /* discussion */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;{{Infobox MATH110 Teams&lt;br /&gt;
| team name = Jura&lt;br /&gt;
| member 1 = [mailto:adam@premierwestmma.com Adam Nguyen]&lt;br /&gt;
| member 2 = Christa Bicego&lt;br /&gt;
| member 3 = [mailto:matthew.hsu@gmail.com Matthew Hsu]&lt;br /&gt;
| member 4 = Shamilla Birring&lt;br /&gt;
}}&lt;br /&gt;
&lt;br /&gt;
==discussion==&lt;br /&gt;
&lt;br /&gt;
Hey guys, I&#039;ve been playing with the &lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
(1/(1+e^-t)) &lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
function and I came to a few conclusions&lt;br /&gt;
&lt;br /&gt;
I was able to modify the function with a few added variables. The new functions becomes:&amp;lt;br&amp;gt;&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
(1(q))/(1+we^(-rt)).&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
q - will determine the horizontal asymptote on the right&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
w - will determine at what y should be when t (or x) is 0&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
r - will determine how quickly or slowly the growth will be.&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
Take a look!&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
- Adam&lt;br /&gt;
&lt;br /&gt;
== Workshop ==&lt;br /&gt;
In workshop L.&lt;br /&gt;
&lt;br /&gt;
== Homework ==&lt;br /&gt;
http://wiki.ubc.ca/Course:MATH110/003/Teams/Jura/Homework/&lt;/div&gt;</summary>
		<author><name>AdamsNguyen</name></author>
	</entry>
	<entry>
		<id>https://wiki.ubc.ca/index.php?title=Course:MATH110/Archive/2010-2011/003/Teams/Jura&amp;diff=71767</id>
		<title>Course:MATH110/Archive/2010-2011/003/Teams/Jura</title>
		<link rel="alternate" type="text/html" href="https://wiki.ubc.ca/index.php?title=Course:MATH110/Archive/2010-2011/003/Teams/Jura&amp;diff=71767"/>
		<updated>2011-01-24T03:13:15Z</updated>

		<summary type="html">&lt;p&gt;AdamsNguyen: /* discussion */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;{{Infobox MATH110 Teams&lt;br /&gt;
| team name = Jura&lt;br /&gt;
| member 1 = [mailto:adam@premierwestmma.com Adam Nguyen]&lt;br /&gt;
| member 2 = Christa Bicego&lt;br /&gt;
| member 3 = [mailto:matthew.hsu@gmail.com Matthew Hsu]&lt;br /&gt;
| member 4 = Shamilla Birring&lt;br /&gt;
}}&lt;br /&gt;
&lt;br /&gt;
==discussion==&lt;br /&gt;
&lt;br /&gt;
Hey guys, I&#039;ve been playing with the &lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
(1/(1+e^-t)) &lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
function and I came to a few conclusions&lt;br /&gt;
&lt;br /&gt;
I was able to modify the function with a few added variables. The new functions becomes:&amp;lt;br&amp;gt;&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
(1(q))/(1+we^(-rt)).&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
q - will determine the horizontal asymptote on the right&lt;br /&gt;
w - will determine at what y should be when t (or x) is 0&lt;br /&gt;
r - will determine how quickly or slowly the growth will be.&lt;br /&gt;
&lt;br /&gt;
Take a look!&lt;br /&gt;
&lt;br /&gt;
- Adam&lt;br /&gt;
&lt;br /&gt;
== Workshop ==&lt;br /&gt;
In workshop L.&lt;br /&gt;
&lt;br /&gt;
== Homework ==&lt;br /&gt;
http://wiki.ubc.ca/Course:MATH110/003/Teams/Jura/Homework/&lt;/div&gt;</summary>
		<author><name>AdamsNguyen</name></author>
	</entry>
	<entry>
		<id>https://wiki.ubc.ca/index.php?title=Course:MATH110/Archive/2010-2011/003/Teams/Jura&amp;diff=71766</id>
		<title>Course:MATH110/Archive/2010-2011/003/Teams/Jura</title>
		<link rel="alternate" type="text/html" href="https://wiki.ubc.ca/index.php?title=Course:MATH110/Archive/2010-2011/003/Teams/Jura&amp;diff=71766"/>
		<updated>2011-01-24T03:12:31Z</updated>

		<summary type="html">&lt;p&gt;AdamsNguyen: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;{{Infobox MATH110 Teams&lt;br /&gt;
| team name = Jura&lt;br /&gt;
| member 1 = [mailto:adam@premierwestmma.com Adam Nguyen]&lt;br /&gt;
| member 2 = Christa Bicego&lt;br /&gt;
| member 3 = [mailto:matthew.hsu@gmail.com Matthew Hsu]&lt;br /&gt;
| member 4 = Shamilla Birring&lt;br /&gt;
}}&lt;br /&gt;
&lt;br /&gt;
==discussion==&lt;br /&gt;
&lt;br /&gt;
Hey guys, I&#039;ve been playing with the (1/(1+e^-t)) functions and I came to a few conclusions&lt;br /&gt;
&lt;br /&gt;
I was able to modify the function with a few added variables. The new functions becomes:&lt;br /&gt;
(1(q))/(1+we^(-rt)).&lt;br /&gt;
q - will determine the horizontal asymptote on the right&lt;br /&gt;
w - will determine at what y should be when t (or x) is 0&lt;br /&gt;
r - will determine how quickly or slowly the growth will be.&lt;br /&gt;
&lt;br /&gt;
Take a look!&lt;br /&gt;
&lt;br /&gt;
- Adam &lt;br /&gt;
&lt;br /&gt;
== Workshop ==&lt;br /&gt;
In workshop L.&lt;br /&gt;
&lt;br /&gt;
== Homework ==&lt;br /&gt;
http://wiki.ubc.ca/Course:MATH110/003/Teams/Jura/Homework/&lt;/div&gt;</summary>
		<author><name>AdamsNguyen</name></author>
	</entry>
	<entry>
		<id>https://wiki.ubc.ca/index.php?title=Course:MATH110/Archive/2010-2011/003/Teams/Jura/Homework/11_Part3&amp;diff=70890</id>
		<title>Course:MATH110/Archive/2010-2011/003/Teams/Jura/Homework/11 Part3</title>
		<link rel="alternate" type="text/html" href="https://wiki.ubc.ca/index.php?title=Course:MATH110/Archive/2010-2011/003/Teams/Jura/Homework/11_Part3&amp;diff=70890"/>
		<updated>2011-01-19T07:49:27Z</updated>

		<summary type="html">&lt;p&gt;AdamsNguyen: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;&amp;lt;p&amp;gt;&amp;lt;b&amp;gt;&amp;lt;i&amp;gt;&lt;br /&gt;
Write a linear model to predict the cost of producing flags of your team&#039;s Canton under the assumptions that the marginal cost is $7 per unit and that at the current production level of 20 items, the cost is $100.&lt;br /&gt;
&amp;lt;/b&amp;gt;&amp;lt;/i&amp;gt;&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
The following linear equation is a model to predict the cost of producing flags of a Canton under the assumption that the marginal cost is $7 per unit and that at the current production level of 20 items, the cost is $100. C(F) = 7F – 40.&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&amp;lt;b&amp;gt;&amp;lt;i&amp;gt;&lt;br /&gt;
Describe your model.&lt;br /&gt;
&amp;lt;/b&amp;gt;&amp;lt;/i&amp;gt;&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
[[File:plot123.gif]]&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&amp;lt;b&amp;gt;&amp;lt;i&amp;gt;&lt;br /&gt;
What does your model predict for a production of 150 items?&lt;br /&gt;
&amp;lt;/b&amp;gt;&amp;lt;/i&amp;gt;&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
This model predicts that at the production of 150 items, the cost $1010.&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&amp;lt;b&amp;gt;&amp;lt;i&amp;gt;&lt;br /&gt;
According to your model, what happens to the average cost per item as production levels increase?&lt;br /&gt;
&amp;lt;/b&amp;gt;&amp;lt;/i&amp;gt;&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
According to this model, the average cost per item will increase as production levels increase.&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&amp;lt;b&amp;gt;&amp;lt;i&amp;gt;&lt;br /&gt;
The average cost remains constant as production increases.&lt;br /&gt;
&amp;lt;/b&amp;gt;&amp;lt;/i&amp;gt;&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
A model with this attribute has a constant slope. Therefore an equation of this type of model would be linear and look like:&amp;lt;br&amp;gt;&lt;br /&gt;
C(F) = XF&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
For example:&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
C(F) = 7F&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
C(F) = F&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&amp;lt;b&amp;gt;&amp;lt;i&amp;gt;&lt;br /&gt;
The average cost diminishes as production increases (-,+)&lt;br /&gt;
&amp;lt;/b&amp;gt;&amp;lt;/i&amp;gt;&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
Average Cost = total cost/production&amp;lt;br&amp;gt;&amp;lt;br&amp;gt;&lt;br /&gt;
A new model example: The marginal cost of a 3D t.v. is $400 dollars per unit at current production of 10 items, the cost is $5000 dollars.&amp;lt;br&amp;gt;&lt;br /&gt;
C(10) = 400(10) + x&amp;lt;br&amp;gt;&lt;br /&gt;
C(10) = 4000 + x&amp;lt;br&amp;gt;&lt;br /&gt;
5000 - 4000 = x&amp;lt;br&amp;gt;&lt;br /&gt;
x = 1000&amp;lt;br&amp;gt;&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
C(F) = 400F + 1000&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Average Cost = total cost/production&amp;lt;br&amp;gt;&lt;br /&gt;
C(10) = 400(10) + 1000 = 5000/10 = 500&amp;lt;br&amp;gt;&lt;br /&gt;
C(20) = 400(20) + 1000 = 9000/20 = 450&amp;lt;br&amp;gt;&lt;br /&gt;
C(25) = 400(25) + 1000 = 11000/25 = 440&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Conclusion: the data shows that the average cost becomes smaller as production increases&amp;lt;br&amp;gt;&lt;br /&gt;
AvgC becomes smaller when Production increases&amp;lt;br&amp;gt;&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&amp;lt;b&amp;gt;&amp;lt;i&amp;gt;&lt;br /&gt;
The average cost increases as production increases.&lt;br /&gt;
&amp;lt;/b&amp;gt;&amp;lt;/i&amp;gt;&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
Average cost becomes larger when Production becomes larger (+,+)&amp;lt;br&amp;gt;&lt;br /&gt;
Average Cost = total cost/production&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
New model: The marginal cost of a pair of runners is $8 dollars per unit and that at the current production level of 50 items, the cost is $200 dollars &amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
C(F) = 8F - 200&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The average cost is getting larger when production becomes larger shown by substituting larger production quantities into the function for F.&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
C(50) = 8(50) - 200 = 200&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
C(51) = 8(51) - 200 = 208&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Average Cost = total cost/production&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
C(50) = 200/50 = 4&amp;lt;br&amp;gt;&lt;br /&gt;
C(51) = 208/51 = 4.07&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
This represents that the function C(F) is increasing and on a graph shows that as one moves up the function both production and average costs are increasing.&amp;lt;br&amp;gt;&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&amp;lt;b&amp;gt;&amp;lt;i&amp;gt;&lt;br /&gt;
You obtain an economy of scale. This means that starting at some specific production level, the marginal cost is always less than the average cost.&lt;br /&gt;
&amp;lt;/b&amp;gt;&amp;lt;/i&amp;gt;&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
Before we begin to describe our model for an economy of scale, it will be helpful to understand exactly what an economy of scale is. With this term being somewhat novel to our group, our research instructed us that economies of scale describes the decreased per unit cost as the number of units of production increases. Basically, it means that when our flag corporation produces a certain amount of flags, that our corporation will realize a reduction in the per unit cost of our flags as our corporation&#039;s production level increases.&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
We can think of this definition contextually by examining Walmart. Walmart is a good example at a corporation that exploits the notion of economies of scale because it purchases its supplies in bulk. This mass purchasing of supplies allows Walmart to buy these supplies at a discount which ultimately allows them to sell their products at a lower cost than most of their competitors.&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
Before we present our model, it will be helpful to explain a few details in order to gain a better understanding in how our model works. Initially, our flag corporation can produce the first 20 flags in an order for $100.00. Any extraneous flags in that particular order will cost us an additional $7.00 per flag. From our above linear model, we can see that any additional extraneous flags actually cost more per unit when compared to the $5.00 per unit we were charged for placing an order of 20 flags. This fact is a bit disturbing because our supplier is punishing us for purchasing more than 20 flags! It&#039;s almost like our supplier does not want us to buy more from them. Because of this fact, our initial figures need to be changed to illustrate the economy of scale phenomena. Rather than punishing us, our supplier makes the following changes to their pricing to encourage bulk purchases. The following changes are illustrated in our chart listed below and one can see that as our production level increases, our cost per unit actually decreases.&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
Here is a following chart that demonstrates the economy of scale phenomena: [[File:110 jura graph.xlsx]]. You can see our formulas by clicking each respective cell in the chart. Feel free to play with the inputs as well. The inputs are shaded brown and the chart will automatically update according to your inputs.&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
One key note that we must address is that the marginal cost per unit should be cheaper than the production level cost per unit because marginal cost is the extra amount we have to pay past our production level. Since we are Jura Corporation, it is honourable for our supplier to reward us with a discount if we buy in bulk! Also, the unit price cannot keep on getting cheaper. Even though Jura Corporation is purchasing in bulk, we will eventually reach a limit where the discounts will remain stable.&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&amp;lt;b&amp;gt;&amp;lt;i&amp;gt;&lt;br /&gt;
Other interesting properties that you can think of and create a model for. &lt;br /&gt;
&amp;lt;/b&amp;gt;&amp;lt;/i&amp;gt;&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
Since we have examined economies of scale, it would be interesting to take the opposite meaning of this definition. That is, as Jura Corporation increases, the per unit cost also increases. It is feasible to imagine that Jura Corporation can become too large for its own good and this increase could actually lead to increase prices.&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
One interesting model that may act as a cost/production model is the family of functions Y=1/x.&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
This would be a good model for selling something on a mass production. For example, If we wanted to sell keychains and it cost us $.25 to make, we can calculate possible prices we can sell them for. In this case we can use a function like Y=100/x. We could say something like there is a minimum order of 40 ($2.50 a keychain) and the more you order the cheaper it would be. Of course, we&#039;ll do a cut off in discount like you&#039;ll stop receiving the discount at 150 keychains ($.67 cents). Now if we wanted to order 120 keychains, we&#039;ll plug 120 into the function and get the value 83.33 cents. So the total price of a wholesale order of 120 keychains would be (120*83.33) $99.60. &lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
Y=100/x&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
[[File:plot2.gif]]&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;/div&gt;</summary>
		<author><name>AdamsNguyen</name></author>
	</entry>
	<entry>
		<id>https://wiki.ubc.ca/index.php?title=File:Plot2.gif&amp;diff=70889</id>
		<title>File:Plot2.gif</title>
		<link rel="alternate" type="text/html" href="https://wiki.ubc.ca/index.php?title=File:Plot2.gif&amp;diff=70889"/>
		<updated>2011-01-19T07:48:32Z</updated>

		<summary type="html">&lt;p&gt;AdamsNguyen: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;&lt;/div&gt;</summary>
		<author><name>AdamsNguyen</name></author>
	</entry>
	<entry>
		<id>https://wiki.ubc.ca/index.php?title=Course:MATH110/Archive/2010-2011/003/Teams/Jura/Homework/11_Part3&amp;diff=70888</id>
		<title>Course:MATH110/Archive/2010-2011/003/Teams/Jura/Homework/11 Part3</title>
		<link rel="alternate" type="text/html" href="https://wiki.ubc.ca/index.php?title=Course:MATH110/Archive/2010-2011/003/Teams/Jura/Homework/11_Part3&amp;diff=70888"/>
		<updated>2011-01-19T07:48:21Z</updated>

		<summary type="html">&lt;p&gt;AdamsNguyen: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;&amp;lt;p&amp;gt;&amp;lt;b&amp;gt;&amp;lt;i&amp;gt;&lt;br /&gt;
Write a linear model to predict the cost of producing flags of your team&#039;s Canton under the assumptions that the marginal cost is $7 per unit and that at the current production level of 20 items, the cost is $100.&lt;br /&gt;
&amp;lt;/b&amp;gt;&amp;lt;/i&amp;gt;&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
The following linear equation is a model to predict the cost of producing flags of a Canton under the assumption that the marginal cost is $7 per unit and that at the current production level of 20 items, the cost is $100. C(F) = 7F – 40.&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&amp;lt;b&amp;gt;&amp;lt;i&amp;gt;&lt;br /&gt;
Describe your model.&lt;br /&gt;
&amp;lt;/b&amp;gt;&amp;lt;/i&amp;gt;&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
[[File:plot123.gif]]&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&amp;lt;b&amp;gt;&amp;lt;i&amp;gt;&lt;br /&gt;
What does your model predict for a production of 150 items?&lt;br /&gt;
&amp;lt;/b&amp;gt;&amp;lt;/i&amp;gt;&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
This model predicts that at the production of 150 items, the cost $1010.&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&amp;lt;b&amp;gt;&amp;lt;i&amp;gt;&lt;br /&gt;
According to your model, what happens to the average cost per item as production levels increase?&lt;br /&gt;
&amp;lt;/b&amp;gt;&amp;lt;/i&amp;gt;&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
According to this model, the average cost per item will increase as production levels increase.&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&amp;lt;b&amp;gt;&amp;lt;i&amp;gt;&lt;br /&gt;
The average cost remains constant as production increases.&lt;br /&gt;
&amp;lt;/b&amp;gt;&amp;lt;/i&amp;gt;&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
A model with this attribute has a constant slope. Therefore an equation of this type of model would be linear and look like:&amp;lt;br&amp;gt;&lt;br /&gt;
C(F) = XF&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
For example:&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
C(F) = 7F&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
C(F) = F&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&amp;lt;b&amp;gt;&amp;lt;i&amp;gt;&lt;br /&gt;
The average cost diminishes as production increases (-,+)&lt;br /&gt;
&amp;lt;/b&amp;gt;&amp;lt;/i&amp;gt;&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
Average Cost = total cost/production&amp;lt;br&amp;gt;&amp;lt;br&amp;gt;&lt;br /&gt;
A new model example: The marginal cost of a 3D t.v. is $400 dollars per unit at current production of 10 items, the cost is $5000 dollars.&amp;lt;br&amp;gt;&lt;br /&gt;
C(10) = 400(10) + x&amp;lt;br&amp;gt;&lt;br /&gt;
C(10) = 4000 + x&amp;lt;br&amp;gt;&lt;br /&gt;
5000 - 4000 = x&amp;lt;br&amp;gt;&lt;br /&gt;
x = 1000&amp;lt;br&amp;gt;&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
C(F) = 400F + 1000&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Average Cost = total cost/production&amp;lt;br&amp;gt;&lt;br /&gt;
C(10) = 400(10) + 1000 = 5000/10 = 500&amp;lt;br&amp;gt;&lt;br /&gt;
C(20) = 400(20) + 1000 = 9000/20 = 450&amp;lt;br&amp;gt;&lt;br /&gt;
C(25) = 400(25) + 1000 = 11000/25 = 440&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Conclusion: the data shows that the average cost becomes smaller as production increases&amp;lt;br&amp;gt;&lt;br /&gt;
AvgC becomes smaller when Production increases&amp;lt;br&amp;gt;&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&amp;lt;b&amp;gt;&amp;lt;i&amp;gt;&lt;br /&gt;
The average cost increases as production increases.&lt;br /&gt;
&amp;lt;/b&amp;gt;&amp;lt;/i&amp;gt;&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
Average cost becomes larger when Production becomes larger (+,+)&amp;lt;br&amp;gt;&lt;br /&gt;
Average Cost = total cost/production&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
New model: The marginal cost of a pair of runners is $8 dollars per unit and that at the current production level of 50 items, the cost is $200 dollars &amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
C(F) = 8F - 200&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The average cost is getting larger when production becomes larger shown by substituting larger production quantities into the function for F.&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
C(50) = 8(50) - 200 = 200&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
C(51) = 8(51) - 200 = 208&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Average Cost = total cost/production&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
C(50) = 200/50 = 4&amp;lt;br&amp;gt;&lt;br /&gt;
C(51) = 208/51 = 4.07&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
This represents that the function C(F) is increasing and on a graph shows that as one moves up the function both production and average costs are increasing.&amp;lt;br&amp;gt;&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&amp;lt;b&amp;gt;&amp;lt;i&amp;gt;&lt;br /&gt;
You obtain an economy of scale. This means that starting at some specific production level, the marginal cost is always less than the average cost.&lt;br /&gt;
&amp;lt;/b&amp;gt;&amp;lt;/i&amp;gt;&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
Before we begin to describe our model for an economy of scale, it will be helpful to understand exactly what an economy of scale is. With this term being somewhat novel to our group, our research instructed us that economies of scale describes the decreased per unit cost as the number of units of production increases. Basically, it means that when our flag corporation produces a certain amount of flags, that our corporation will realize a reduction in the per unit cost of our flags as our corporation&#039;s production level increases.&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
We can think of this definition contextually by examining Walmart. Walmart is a good example at a corporation that exploits the notion of economies of scale because it purchases its supplies in bulk. This mass purchasing of supplies allows Walmart to buy these supplies at a discount which ultimately allows them to sell their products at a lower cost than most of their competitors.&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
Before we present our model, it will be helpful to explain a few details in order to gain a better understanding in how our model works. Initially, our flag corporation can produce the first 20 flags in an order for $100.00. Any extraneous flags in that particular order will cost us an additional $7.00 per flag. From our above linear model, we can see that any additional extraneous flags actually cost more per unit when compared to the $5.00 per unit we were charged for placing an order of 20 flags. This fact is a bit disturbing because our supplier is punishing us for purchasing more than 20 flags! It&#039;s almost like our supplier does not want us to buy more from them. Because of this fact, our initial figures need to be changed to illustrate the economy of scale phenomena. Rather than punishing us, our supplier makes the following changes to their pricing to encourage bulk purchases. The following changes are illustrated in our chart listed below and one can see that as our production level increases, our cost per unit actually decreases.&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
Here is a following chart that demonstrates the economy of scale phenomena: [[File:110 jura graph.xlsx]]. You can see our formulas by clicking each respective cell in the chart. Feel free to play with the inputs as well. The inputs are shaded brown and the chart will automatically update according to your inputs.&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
One key note that we must address is that the marginal cost per unit should be cheaper than the production level cost per unit because marginal cost is the extra amount we have to pay past our production level. Since we are Jura Corporation, it is honourable for our supplier to reward us with a discount if we buy in bulk! Also, the unit price cannot keep on getting cheaper. Even though Jura Corporation is purchasing in bulk, we will eventually reach a limit where the discounts will remain stable.&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&amp;lt;b&amp;gt;&amp;lt;i&amp;gt;&lt;br /&gt;
Other interesting properties that you can think of and create a model for. &lt;br /&gt;
&amp;lt;/b&amp;gt;&amp;lt;/i&amp;gt;&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
Since we have examined economies of scale, it would be interesting to take the opposite meaning of this definition. That is, as Jura Corporation increases, the per unit cost also increases. It is feasible to imagine that Jura Corporation can become too large for its own good and this increase could actually lead to increase prices.&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
One interesting model that may act as a cost/production model is the family of functions Y=1/x.&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
This would be a good model for selling something on a mass production. For example, If we wanted to sell keychains and it cost us $.25 to make, we can calculate possible prices we can sell them for. In this case we can use a function like Y=100/x. We could say something like there is a minimum order of 40 ($2.50 a keychain) and the more you order the cheaper it would be. Of course, we&#039;ll do a cut off in discount like you&#039;ll stop receiving the discount at 150 keychains ($.67 cents). Now if we wanted to order 120 keychains, we&#039;ll plug 120 into the function and get the value 83.33 cents. So the total price of a wholesale order of 120 keychains would be (120*83.33) $99.60. &lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
[[File:plot2.gif]]&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;/div&gt;</summary>
		<author><name>AdamsNguyen</name></author>
	</entry>
	<entry>
		<id>https://wiki.ubc.ca/index.php?title=Course:MATH110/Archive/2010-2011/003/Teams/Jura/Homework/11_Part3&amp;diff=70887</id>
		<title>Course:MATH110/Archive/2010-2011/003/Teams/Jura/Homework/11 Part3</title>
		<link rel="alternate" type="text/html" href="https://wiki.ubc.ca/index.php?title=Course:MATH110/Archive/2010-2011/003/Teams/Jura/Homework/11_Part3&amp;diff=70887"/>
		<updated>2011-01-19T07:45:11Z</updated>

		<summary type="html">&lt;p&gt;AdamsNguyen: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;&amp;lt;p&amp;gt;&amp;lt;b&amp;gt;&amp;lt;i&amp;gt;&lt;br /&gt;
Write a linear model to predict the cost of producing flags of your team&#039;s Canton under the assumptions that the marginal cost is $7 per unit and that at the current production level of 20 items, the cost is $100.&lt;br /&gt;
&amp;lt;/b&amp;gt;&amp;lt;/i&amp;gt;&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
The following linear equation is a model to predict the cost of producing flags of a Canton under the assumption that the marginal cost is $7 per unit and that at the current production level of 20 items, the cost is $100. C(F) = 7F – 40.&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&amp;lt;b&amp;gt;&amp;lt;i&amp;gt;&lt;br /&gt;
Describe your model.&lt;br /&gt;
&amp;lt;/b&amp;gt;&amp;lt;/i&amp;gt;&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
[[File:plot123.gif]]&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&amp;lt;b&amp;gt;&amp;lt;i&amp;gt;&lt;br /&gt;
What does your model predict for a production of 150 items?&lt;br /&gt;
&amp;lt;/b&amp;gt;&amp;lt;/i&amp;gt;&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
This model predicts that at the production of 150 items, the cost $1010.&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&amp;lt;b&amp;gt;&amp;lt;i&amp;gt;&lt;br /&gt;
According to your model, what happens to the average cost per item as production levels increase?&lt;br /&gt;
&amp;lt;/b&amp;gt;&amp;lt;/i&amp;gt;&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
According to this model, the average cost per item will increase as production levels increase.&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&amp;lt;b&amp;gt;&amp;lt;i&amp;gt;&lt;br /&gt;
The average cost remains constant as production increases.&lt;br /&gt;
&amp;lt;/b&amp;gt;&amp;lt;/i&amp;gt;&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
A model with this attribute has a constant slope. Therefore an equation of this type of model would be linear and look like:&amp;lt;br&amp;gt;&lt;br /&gt;
C(F) = XF&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
For example:&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
C(F) = 7F&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
C(F) = F&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&amp;lt;b&amp;gt;&amp;lt;i&amp;gt;&lt;br /&gt;
The average cost diminishes as production increases (-,+)&lt;br /&gt;
&amp;lt;/b&amp;gt;&amp;lt;/i&amp;gt;&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
Average Cost = total cost/production&amp;lt;br&amp;gt;&amp;lt;br&amp;gt;&lt;br /&gt;
A new model example: The marginal cost of a 3D t.v. is $400 dollars per unit at current production of 10 items, the cost is $5000 dollars.&amp;lt;br&amp;gt;&lt;br /&gt;
C(10) = 400(10) + x&amp;lt;br&amp;gt;&lt;br /&gt;
C(10) = 4000 + x&amp;lt;br&amp;gt;&lt;br /&gt;
5000 - 4000 = x&amp;lt;br&amp;gt;&lt;br /&gt;
x = 1000&amp;lt;br&amp;gt;&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
C(F) = 400F + 1000&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Average Cost = total cost/production&amp;lt;br&amp;gt;&lt;br /&gt;
C(10) = 400(10) + 1000 = 5000/10 = 500&amp;lt;br&amp;gt;&lt;br /&gt;
C(20) = 400(20) + 1000 = 9000/20 = 450&amp;lt;br&amp;gt;&lt;br /&gt;
C(25) = 400(25) + 1000 = 11000/25 = 440&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Conclusion: the data shows that the average cost becomes smaller as production increases&amp;lt;br&amp;gt;&lt;br /&gt;
AvgC becomes smaller when Production increases&amp;lt;br&amp;gt;&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&amp;lt;b&amp;gt;&amp;lt;i&amp;gt;&lt;br /&gt;
The average cost increases as production increases.&lt;br /&gt;
&amp;lt;/b&amp;gt;&amp;lt;/i&amp;gt;&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
Average cost becomes larger when Production becomes larger (+,+)&amp;lt;br&amp;gt;&lt;br /&gt;
Average Cost = total cost/production&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
New model: The marginal cost of a pair of runners is $8 dollars per unit and that at the current production level of 50 items, the cost is $200 dollars &amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
C(F) = 8F - 200&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The average cost is getting larger when production becomes larger shown by substituting larger production quantities into the function for F.&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
C(50) = 8(50) - 200 = 200&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
C(51) = 8(51) - 200 = 208&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Average Cost = total cost/production&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
C(50) = 200/50 = 4&amp;lt;br&amp;gt;&lt;br /&gt;
C(51) = 208/51 = 4.07&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
This represents that the function C(F) is increasing and on a graph shows that as one moves up the function both production and average costs are increasing.&amp;lt;br&amp;gt;&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&amp;lt;b&amp;gt;&amp;lt;i&amp;gt;&lt;br /&gt;
You obtain an economy of scale. This means that starting at some specific production level, the marginal cost is always less than the average cost.&lt;br /&gt;
&amp;lt;/b&amp;gt;&amp;lt;/i&amp;gt;&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
Before we begin to describe our model for an economy of scale, it will be helpful to understand exactly what an economy of scale is. With this term being somewhat novel to our group, our research instructed us that economies of scale describes the decreased per unit cost as the number of units of production increases. Basically, it means that when our flag corporation produces a certain amount of flags, that our corporation will realize a reduction in the per unit cost of our flags as our corporation&#039;s production level increases.&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
We can think of this definition contextually by examining Walmart. Walmart is a good example at a corporation that exploits the notion of economies of scale because it purchases its supplies in bulk. This mass purchasing of supplies allows Walmart to buy these supplies at a discount which ultimately allows them to sell their products at a lower cost than most of their competitors.&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
Before we present our model, it will be helpful to explain a few details in order to gain a better understanding in how our model works. Initially, our flag corporation can produce the first 20 flags in an order for $100.00. Any extraneous flags in that particular order will cost us an additional $7.00 per flag. From our above linear model, we can see that any additional extraneous flags actually cost more per unit when compared to the $5.00 per unit we were charged for placing an order of 20 flags. This fact is a bit disturbing because our supplier is punishing us for purchasing more than 20 flags! It&#039;s almost like our supplier does not want us to buy more from them. Because of this fact, our initial figures need to be changed to illustrate the economy of scale phenomena. Rather than punishing us, our supplier makes the following changes to their pricing to encourage bulk purchases. The following changes are illustrated in our chart listed below and one can see that as our production level increases, our cost per unit actually decreases.&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
Here is a following chart that demonstrates the economy of scale phenomena: [[File:110 jura graph.xlsx]]. You can see our formulas by clicking each respective cell in the chart. Feel free to play with the inputs as well. The inputs are shaded brown and the chart will automatically update according to your inputs.&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
One key note that we must address is that the marginal cost per unit should be cheaper than the production level cost per unit because marginal cost is the extra amount we have to pay past our production level. Since we are Jura Corporation, it is honourable for our supplier to reward us with a discount if we buy in bulk! Also, the unit price cannot keep on getting cheaper. Even though Jura Corporation is purchasing in bulk, we will eventually reach a limit where the discounts will remain stable.&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&amp;lt;b&amp;gt;&amp;lt;i&amp;gt;&lt;br /&gt;
Other interesting properties that you can think of and create a model for. &lt;br /&gt;
&amp;lt;/b&amp;gt;&amp;lt;/i&amp;gt;&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
Since we have examined economies of scale, it would be interesting to take the opposite meaning of this definition. That is, as Jura Corporation increases, the per unit cost also increases. It is feasible to imagine that Jura Corporation can become too large for its own good and this increase could actually lead to increase prices.&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
One interesting model that may act as a cost/production model is the family of functions Y=1/x.&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
This would be a good model for selling something on a mass production. For example, If we wanted to sell keychains and it cost us $.25 to make, we can calculate possible prices we can sell them for. In this case we can use a function like Y=100/x. We could say something like there is a minimum order of 40 ($2.50 a keychain) and the more you order the cheaper it would be. Of course, we&#039;ll do a cut off in discount like you&#039;ll stop receiving the discount at 150 keychains ($.67 cents). Now if we wanted to order 120 keychains, we&#039;ll plug 120 into the function and get the value 83.33 cents. So the total price of a wholesale order of 120 keychains would be (120*83.33) $99.60. &lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;/div&gt;</summary>
		<author><name>AdamsNguyen</name></author>
	</entry>
	<entry>
		<id>https://wiki.ubc.ca/index.php?title=Course:MATH110/Archive/2010-2011/003/Teams/Jura/Homework/11_Part3&amp;diff=70869</id>
		<title>Course:MATH110/Archive/2010-2011/003/Teams/Jura/Homework/11 Part3</title>
		<link rel="alternate" type="text/html" href="https://wiki.ubc.ca/index.php?title=Course:MATH110/Archive/2010-2011/003/Teams/Jura/Homework/11_Part3&amp;diff=70869"/>
		<updated>2011-01-19T07:25:15Z</updated>

		<summary type="html">&lt;p&gt;AdamsNguyen: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;&amp;lt;p&amp;gt;&amp;lt;b&amp;gt;&amp;lt;i&amp;gt;&lt;br /&gt;
Write a linear model to predict the cost of producing flags of your team&#039;s Canton under the assumptions that the marginal cost is $7 per unit and that at the current production level of 20 items, the cost is $100.&lt;br /&gt;
&amp;lt;/b&amp;gt;&amp;lt;/i&amp;gt;&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
The following linear equation is a model to predict the cost of producing flags of a Canton under the assumption that the marginal cost is $7 per unit and that at the current production level of 20 items, the cost is $100. C(F) = 7F – 40.&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&amp;lt;b&amp;gt;&amp;lt;i&amp;gt;&lt;br /&gt;
Describe your model.&lt;br /&gt;
&amp;lt;/b&amp;gt;&amp;lt;/i&amp;gt;&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
[[File:plot123.gif]]&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&amp;lt;b&amp;gt;&amp;lt;i&amp;gt;&lt;br /&gt;
What does your model predict for a production of 150 items?&lt;br /&gt;
&amp;lt;/b&amp;gt;&amp;lt;/i&amp;gt;&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
This model predicts that at the production of 150 items, the cost $1010.&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&amp;lt;b&amp;gt;&amp;lt;i&amp;gt;&lt;br /&gt;
According to your model, what happens to the average cost per item as production levels increase?&lt;br /&gt;
&amp;lt;/b&amp;gt;&amp;lt;/i&amp;gt;&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
According to this model, the average cost per item will increase as production levels increase.&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&amp;lt;b&amp;gt;&amp;lt;i&amp;gt;&lt;br /&gt;
The average cost remains constant as production increases.&lt;br /&gt;
&amp;lt;/b&amp;gt;&amp;lt;/i&amp;gt;&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
A model with this attribute has a constant slope. Therefore an equation of this type of model would be linear and look like:&amp;lt;br&amp;gt;&lt;br /&gt;
C(F) = XF&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
For example:&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
C(F) = 7F&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
C(F) = F&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&amp;lt;b&amp;gt;&amp;lt;i&amp;gt;&lt;br /&gt;
The average cost diminishes as production increases (-,+)&lt;br /&gt;
&amp;lt;/b&amp;gt;&amp;lt;/i&amp;gt;&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
Average Cost = total cost/production&amp;lt;br&amp;gt;&amp;lt;br&amp;gt;&lt;br /&gt;
A new model example: The marginal cost of a 3D t.v. is $400 dollars per unit at current production of 10 items, the cost is $5000 dollars.&amp;lt;br&amp;gt;&lt;br /&gt;
C(10) = 400(10) + x&amp;lt;br&amp;gt;&lt;br /&gt;
C(10) = 4000 + x&amp;lt;br&amp;gt;&lt;br /&gt;
5000 - 4000 = x&amp;lt;br&amp;gt;&lt;br /&gt;
x = 1000&amp;lt;br&amp;gt;&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
C(F) = 400F + 1000&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Average Cost = total cost/production&amp;lt;br&amp;gt;&lt;br /&gt;
C(10) = 400(10) + 1000 = 5000/10 = 500&amp;lt;br&amp;gt;&lt;br /&gt;
C(20) = 400(20) + 1000 = 9000/20 = 450&amp;lt;br&amp;gt;&lt;br /&gt;
C(25) = 400(25) + 1000 = 11000/25 = 440&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Conclusion: the data shows that the average cost becomes smaller as production increases&amp;lt;br&amp;gt;&lt;br /&gt;
AvgC becomes smaller when Production increases&amp;lt;br&amp;gt;&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&amp;lt;b&amp;gt;&amp;lt;i&amp;gt;&lt;br /&gt;
The average cost increases as production increases.&lt;br /&gt;
&amp;lt;/b&amp;gt;&amp;lt;/i&amp;gt;&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
Average cost becomes larger when Production becomes larger (+,+)&amp;lt;br&amp;gt;&lt;br /&gt;
Average Cost = total cost/production&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
New model: The marginal cost of a pair of runners is $8 dollars per unit and that at the current production level of 50 items, the cost is $200 dollars &amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
C(F) = 8F - 200&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The average cost is getting larger when production becomes larger shown by substituting larger production quantities into the function for F.&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
C(50) = 8(50) - 200 = 200&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
C(51) = 8(51) - 200 = 208&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Average Cost = total cost/production&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
C(50) = 200/50 = 4&amp;lt;br&amp;gt;&lt;br /&gt;
C(51) = 208/51 = 4.07&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
This represents that the function C(F) is increasing and on a graph shows that as one moves up the function both production and average costs are increasing.&amp;lt;br&amp;gt;&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&amp;lt;b&amp;gt;&amp;lt;i&amp;gt;&lt;br /&gt;
You obtain an economy of scale. This means that starting at some specific production level, the marginal cost is always less than the average cost.&lt;br /&gt;
&amp;lt;/b&amp;gt;&amp;lt;/i&amp;gt;&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
Before we begin to describe our model for an economy of scale, it will be helpful to understand exactly what an economy of scale is. With this term being somewhat novel to our group, our research instructed us that economies of scale describes the decreased per unit cost as the number of units of production increases. Basically, it means that when our flag corporation produces a certain amount of flags, that our corporation will realize a reduction in the per unit cost of our flags as our corporation&#039;s production level increases.&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
We can think of this definition contextually by examining Walmart. Walmart is a good example at a corporation that exploits the notion of economies of scale because it purchases its supplies in bulk. This mass purchasing of supplies allows Walmart to buy these supplies at a discount which ultimately allows them to sell their products at a lower cost than most of their competitors.&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
Before we present our model, it will be helpful to explain a few details in order to gain a better understanding in how our model works. Initially, our flag corporation can produce the first 20 flags in an order for $100.00. Any extraneous flags in that particular order will cost us an additional $7.00 per flag. From our above linear model, we can see that any additional extraneous flags actually cost more per unit when compared to the $5.00 per unit we were charged for placing an order of 20 flags. This fact is a bit disturbing because our supplier is punishing us for purchasing more than 20 flags! It&#039;s almost like our supplier does not want us to buy more from them. Because of this fact, our initial figures need to be changed to illustrate the economy of scale phenomena. Rather than punishing us, our supplier makes the following changes to their pricing to encourage bulk purchases. The following changes are illustrated in our chart listed below and one can see that as our production level increases, our cost per unit actually decreases.&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
Here is a following chart that demonstrates the economy of scale phenomena: [[File:110 jura graph.xlsx]]. You can see our formulas by clicking each respective cell in the chart. Feel free to play with the inputs as well. The inputs are shaded brown and the chart will automatically update according to your inputs.&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
One key note that we must address is that the marginal cost per unit should be cheaper than the production level cost per unit because marginal cost is the extra amount we have to pay past our production level. Since we are Jura Corporation, it is honourable for our supplier to reward us with a discount if we buy in bulk! Also, the unit price cannot keep on getting cheaper. Even though Jura Corporation is purchasing in bulk, we will eventually reach a limit where the discounts will remain stable.&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&amp;lt;b&amp;gt;&amp;lt;i&amp;gt;&lt;br /&gt;
Other interesting properties that you can think of and create a model for. &lt;br /&gt;
&amp;lt;/b&amp;gt;&amp;lt;/i&amp;gt;&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
Since we have examined economies of scale, it would be interesting to take the opposite meaning of this definition. That is, as Jura Corporation increases, the per unit cost also increases. It is feasible to imagine that Jura Corporation can become too large for its own good and this increase could actually lead to increase prices.&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;/div&gt;</summary>
		<author><name>AdamsNguyen</name></author>
	</entry>
	<entry>
		<id>https://wiki.ubc.ca/index.php?title=Course:MATH110/Archive/2010-2011/003/Teams/Jura/Homework/11_Part3&amp;diff=70821</id>
		<title>Course:MATH110/Archive/2010-2011/003/Teams/Jura/Homework/11 Part3</title>
		<link rel="alternate" type="text/html" href="https://wiki.ubc.ca/index.php?title=Course:MATH110/Archive/2010-2011/003/Teams/Jura/Homework/11_Part3&amp;diff=70821"/>
		<updated>2011-01-19T06:21:59Z</updated>

		<summary type="html">&lt;p&gt;AdamsNguyen: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;&amp;lt;p&amp;gt;&amp;lt;b&amp;gt;&amp;lt;i&amp;gt;&lt;br /&gt;
Write a linear model to predict the cost of producing flags of your team&#039;s Canton under the assumptions that the marginal cost is $7 per unit and that at the current production level of 20 items, the cost is $100.&lt;br /&gt;
&amp;lt;/b&amp;gt;&amp;lt;/i&amp;gt;&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
The following linear equation is a model to predict the cost of producing flags of a Canton under the assumption that the marginal cost is $7 per unit and that at the current production level of 20 items, the cost is $100. C(F) = 7F – 40.&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&amp;lt;b&amp;gt;&amp;lt;i&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Describe your model.&lt;br /&gt;
&amp;lt;/b&amp;gt;&amp;lt;/i&amp;gt;&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
[[File:plot123.gif]]&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&amp;lt;b&amp;gt;&amp;lt;i&amp;gt;&lt;br /&gt;
What does your model predict for a production of 150 items?&lt;br /&gt;
&amp;lt;/b&amp;gt;&amp;lt;/i&amp;gt;&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
This model predicts that at the production of 150 items, the cost $1010.&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&amp;lt;b&amp;gt;&amp;lt;i&amp;gt;&lt;br /&gt;
According to your model, what happens to the average cost per item as production levels increase?&lt;br /&gt;
&amp;lt;/b&amp;gt;&amp;lt;/i&amp;gt;&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
According to this model, the average cost per item will increase as production levels increase.&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&amp;lt;b&amp;gt;&amp;lt;i&amp;gt;&lt;br /&gt;
The average cost remains constant as production increases.&lt;br /&gt;
&amp;lt;/b&amp;gt;&amp;lt;/i&amp;gt;&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
A model with this attribute intersects the origin and has a constant slope. Therefore an equation of this type of model would be linear and look like:&amp;lt;br&amp;gt;&lt;br /&gt;
C(F) = XF&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
For example:&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
C(F) = 7F&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
C(F) = F&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&amp;lt;b&amp;gt;&amp;lt;i&amp;gt;&lt;br /&gt;
The average cost diminishes as production increases (-,+)&lt;br /&gt;
&amp;lt;/b&amp;gt;&amp;lt;/i&amp;gt;&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Average Cost= total cost/ production&amp;lt;br /&amp;gt;&lt;br /&gt;
&amp;lt;br /&amp;gt;&lt;br /&gt;
A new model example: The marginal cost of a 3D t.v. is $400 dollars per unit at current production of 10 items, the cost is $5000 dollars.&amp;lt;br /&amp;gt;&lt;br /&gt;
C(10)= 400(10)+ x&amp;lt;br /&amp;gt;&lt;br /&gt;
C(10) = 4000 + x&amp;lt;br /&amp;gt;&lt;br /&gt;
5000- 4000 = x&amp;lt;br /&amp;gt;&lt;br /&gt;
x= 1000&amp;lt;br /&amp;gt;&lt;br /&gt;
&amp;lt;br /&amp;gt;&lt;br /&gt;
C(F)= 400F + 1000&amp;lt;br /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Average Cost= total cost/ production&amp;lt;br /&amp;gt;&lt;br /&gt;
C(10)= 400(10) +1000 = 5000/10 = 500&amp;lt;br /&amp;gt;&lt;br /&gt;
C(20) = 400(20) +1000 = 9000/20 = 450&amp;lt;br /&amp;gt;&lt;br /&gt;
C(25)= 400(25) +1000 = 11000/ 25 = 440&amp;lt;br /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Conclusion: the data shows that the average cost becomes smaller as production increases&amp;lt;br /&amp;gt;&lt;br /&gt;
AvgC becomes smaller when Production increases&amp;lt;br /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&amp;lt;b&amp;gt;&amp;lt;i&amp;gt;&lt;br /&gt;
The average cost increases as production increases.&lt;br /&gt;
&amp;lt;/b&amp;gt;&amp;lt;/i&amp;gt;&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
Average cost becomes larger when Production becomes larger ( +,+)&amp;lt;br /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Average Cost= total cost/ production&amp;lt;br /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
 new model: The marginal cost of a pair of runners is $8 dollars per unit and that at the current production level of 50 items, the cost is $200 dollars &amp;lt;br /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
C(F)= 8F - 200&amp;lt;br /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The average cost is getting larger when production becomes larger shown by substituting larger production quantities into the function for F.&amp;lt;br /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
C(50)= 8(50)- 200 = 200&amp;lt;br /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
C(51)= 8(51)- 200 = 208&amp;lt;br /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Average Cost= total cost/ production&amp;lt;br /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
C(50)= 200/ 50 = 4&amp;lt;br /&amp;gt;&lt;br /&gt;
C(51)= 208/51 = 4.07&amp;lt;br /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
This represents that the function C(F) is increasing and on a graph shows that as one moves up the function both production and average costs are increasing.&amp;lt;br /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&amp;lt;b&amp;gt;&amp;lt;i&amp;gt;&lt;br /&gt;
You obtain an economy of scale. This means that starting at some specific production level, the marginal cost is always less than the average cost.&lt;br /&gt;
&amp;lt;/b&amp;gt;&amp;lt;/i&amp;gt;&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
Before we begin to describe our model for an economy of scale, it will be helpful to understand exactly what an economy of scale is. With this term being somewhat novel to our group, our research instructed us that economies of scale describes the decreased per unit cost as the number of units of production increases. Basically, it means that when our flag corporation produces a certain amount of flags, that our corporation will realize a reduction in the per unit cost of our flags as our corporation&#039;s production level increases.&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
We can think of this definition contextually by examining Walmart. Walmart is a good example at a corporation that exploits the notion of economies of scale because it purchases its supplies in bulk. This mass purchasing of supplies allows Walmart to buy these supplies at a discount which ultimately allows them to sell their products at a lower cost than most of their competitors.&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
Before we present our model, it will be helpful to explain a few details in order to gain a better understanding in how our model works. Initially, our flag corporation can produce the first 20 flags in an order for $100.00. Any extraneous flags in that particular order will cost us an additional $7.00 per flag. From our above linear model, we can see that any additional extraneous flags actually cost more per unit when compared to the $5.00 per unit we were charged for placing an order of 20 flags. This fact is a bit disturbing because our supplier is punishing us for purchasing more than 20 flags! It&#039;s almost like our supplier does not want us to buy more from them. Because of this fact, our initial figures need to be changed to illustrate the economy of scale phenomena. Rather than punishing us, our supplier makes the following changes to their pricing to encourage bulk purchases. The following changes are illustrated in our chart listed below and one can see that as our production level increases, our cost per unit actually decreases.&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
Here is a following chart that demonstrates the economy of scale phenomena: [[File:110 jura graph.xlsx]]. You can see our formulas by clicking each respective cell in the chart. Feel free to play with the inputs as well. The inputs are shaded brown and the chart will automatically update according to your inputs.&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
One key note that we must address is that the marginal cost per unit should be cheaper than the production level cost per unit because marginal cost is the extra amount we have to pay past our production level. Since we are Jura Corporation, it is honourable for our supplier to reward us with a discount if we buy in bulk! Also, the unit price cannot keep on getting cheaper. Even though Jura Corporation is purchasing in bulk, we will eventually reach a limit where the discounts will remain stable.&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
&amp;lt;i&amp;gt;I&#039;ll need to manually graph this out and scan it in.&amp;lt;/i&amp;gt;&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&amp;lt;b&amp;gt;&amp;lt;i&amp;gt;&lt;br /&gt;
Other interesting properties that you can think of and create a model for. &lt;br /&gt;
&amp;lt;/b&amp;gt;&amp;lt;/i&amp;gt;&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
Solution goes here.&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
== Discussion ==&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
Hello, team Jura. This is Adam, your  new teammate. As you may be aware, there is a team question that is posted. Please take a look and be familiar with the question. We are to write a comprehensive essay on the given problem. To complete this assignment, I propose that we each pick a few points, study those points and write a paragraph on them (ex. Someone can describe the model and find out the cost of 150 units etc.) We&#039;ll then combine our information and I&#039;ll volunteer to write up a good copy.&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
I have already finished the first 4 points &lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
Describe your model.&lt;br /&gt;
What does your model predict for a production of 150 items?&lt;br /&gt;
According yo your model, what happens to the average cost per item as production levels increase?&lt;br /&gt;
Finally, find some other models (not necessarily linear) for which you get other behaviours such as:&lt;br /&gt;
The average cost remains constant as production increases.&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
I&#039;ll leave up to you guys to the rest. Just pick a point or two to study. &lt;br /&gt;
Remember, there is a group evaluation at the end. Please participate so I can give each of you guys 100% in participation marks at the end.&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
Alright guys, lets start this year with a blast!&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
-Adam Nguyen&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
I will do the next two points from where Adam left off tonight - that leaves the last 2 points.&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
-Christa Bicego&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
Since there are two points left, I&#039;ll work on the Economies of Scale model.&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
-Matthew&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
Alright, I have the framework for our economy of scale question. I think it&#039;s correct, but any feedback on it would be appreciated. If everything looks alright, I&#039;ll finish the graph and scan it in. If you need to contact me, feel free to email me. I just posted my contact information on our Wiki.&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
-Matthew&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
Just did some formatting on our page to give it some structure. If you&#039;re unfamiliar with posting on the Wiki, I&#039;ve templated where you can copy and paste your responses into to make things a bit easier.&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
-Matthew&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;/div&gt;</summary>
		<author><name>AdamsNguyen</name></author>
	</entry>
	<entry>
		<id>https://wiki.ubc.ca/index.php?title=Course:MATH110/Archive/2010-2011/003/Teams/Jura/Homework/11_Part3&amp;diff=70820</id>
		<title>Course:MATH110/Archive/2010-2011/003/Teams/Jura/Homework/11 Part3</title>
		<link rel="alternate" type="text/html" href="https://wiki.ubc.ca/index.php?title=Course:MATH110/Archive/2010-2011/003/Teams/Jura/Homework/11_Part3&amp;diff=70820"/>
		<updated>2011-01-19T06:20:57Z</updated>

		<summary type="html">&lt;p&gt;AdamsNguyen: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;&amp;lt;p&amp;gt;&amp;lt;b&amp;gt;&amp;lt;i&amp;gt;&lt;br /&gt;
Write a linear model to predict the cost of producing flags of your team&#039;s Canton under the assumptions that the marginal cost is $7 per unit and that at the current production level of 20 items, the cost is $100.&lt;br /&gt;
&amp;lt;/b&amp;gt;&amp;lt;/i&amp;gt;&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
The following linear equation is a model to predict the cost of producing flags of a Canton under the assumption that the marginal cost is $7 per unit and that at the current production level of 20 items, the cost is $100. C(F) = 7F – 40.&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&amp;lt;b&amp;gt;&amp;lt;i&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Describe your model.&lt;br /&gt;
&amp;lt;/b&amp;gt;&amp;lt;/i&amp;gt;&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
[[File:plot123.gif]]&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&amp;lt;b&amp;gt;&amp;lt;i&amp;gt;&lt;br /&gt;
What does your model predict for a production of 150 items?&lt;br /&gt;
&amp;lt;/b&amp;gt;&amp;lt;/i&amp;gt;&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
This model predicts that at the production of 150 items, the cost $1010.&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&amp;lt;b&amp;gt;&amp;lt;i&amp;gt;&lt;br /&gt;
According to your model, what happens to the average cost per item as production levels increase?&lt;br /&gt;
&amp;lt;/b&amp;gt;&amp;lt;/i&amp;gt;&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
According to this model, the average cost per item will increase as production levels increase.&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&amp;lt;b&amp;gt;&amp;lt;i&amp;gt;&lt;br /&gt;
The average cost remains constant as production increases.&lt;br /&gt;
&amp;lt;/b&amp;gt;&amp;lt;/i&amp;gt;&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
A model with this attribute intersects the origin and has a constant slope. Therefore an equation of this type of model would look like:&amp;lt;br&amp;gt;&lt;br /&gt;
C(F) = XF&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
For example:&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
C(F) = 7F&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
C(F) = F&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&amp;lt;b&amp;gt;&amp;lt;i&amp;gt;&lt;br /&gt;
The average cost diminishes as production increases (-,+)&lt;br /&gt;
&amp;lt;/b&amp;gt;&amp;lt;/i&amp;gt;&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Average Cost= total cost/ production&amp;lt;br /&amp;gt;&lt;br /&gt;
&amp;lt;br /&amp;gt;&lt;br /&gt;
A new model example: The marginal cost of a 3D t.v. is $400 dollars per unit at current production of 10 items, the cost is $5000 dollars.&amp;lt;br /&amp;gt;&lt;br /&gt;
C(10)= 400(10)+ x&amp;lt;br /&amp;gt;&lt;br /&gt;
C(10) = 4000 + x&amp;lt;br /&amp;gt;&lt;br /&gt;
5000- 4000 = x&amp;lt;br /&amp;gt;&lt;br /&gt;
x= 1000&amp;lt;br /&amp;gt;&lt;br /&gt;
&amp;lt;br /&amp;gt;&lt;br /&gt;
C(F)= 400F + 1000&amp;lt;br /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Average Cost= total cost/ production&amp;lt;br /&amp;gt;&lt;br /&gt;
C(10)= 400(10) +1000 = 5000/10 = 500&amp;lt;br /&amp;gt;&lt;br /&gt;
C(20) = 400(20) +1000 = 9000/20 = 450&amp;lt;br /&amp;gt;&lt;br /&gt;
C(25)= 400(25) +1000 = 11000/ 25 = 440&amp;lt;br /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Conclusion: the data shows that the average cost becomes smaller as production increases&amp;lt;br /&amp;gt;&lt;br /&gt;
AvgC becomes smaller when Production increases&amp;lt;br /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&amp;lt;b&amp;gt;&amp;lt;i&amp;gt;&lt;br /&gt;
The average cost increases as production increases.&lt;br /&gt;
&amp;lt;/b&amp;gt;&amp;lt;/i&amp;gt;&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
Average cost becomes larger when Production becomes larger ( +,+)&amp;lt;br /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Average Cost= total cost/ production&amp;lt;br /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
 new model: The marginal cost of a pair of runners is $8 dollars per unit and that at the current production level of 50 items, the cost is $200 dollars &amp;lt;br /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
C(F)= 8F - 200&amp;lt;br /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The average cost is getting larger when production becomes larger shown by substituting larger production quantities into the function for F.&amp;lt;br /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
C(50)= 8(50)- 200 = 200&amp;lt;br /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
C(51)= 8(51)- 200 = 208&amp;lt;br /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Average Cost= total cost/ production&amp;lt;br /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
C(50)= 200/ 50 = 4&amp;lt;br /&amp;gt;&lt;br /&gt;
C(51)= 208/51 = 4.07&amp;lt;br /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
This represents that the function C(F) is increasing and on a graph shows that as one moves up the function both production and average costs are increasing.&amp;lt;br /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&amp;lt;b&amp;gt;&amp;lt;i&amp;gt;&lt;br /&gt;
You obtain an economy of scale. This means that starting at some specific production level, the marginal cost is always less than the average cost.&lt;br /&gt;
&amp;lt;/b&amp;gt;&amp;lt;/i&amp;gt;&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
Before we begin to describe our model for an economy of scale, it will be helpful to understand exactly what an economy of scale is. With this term being somewhat novel to our group, our research instructed us that economies of scale describes the decreased per unit cost as the number of units of production increases. Basically, it means that when our flag corporation produces a certain amount of flags, that our corporation will realize a reduction in the per unit cost of our flags as our corporation&#039;s production level increases.&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
We can think of this definition contextually by examining Walmart. Walmart is a good example at a corporation that exploits the notion of economies of scale because it purchases its supplies in bulk. This mass purchasing of supplies allows Walmart to buy these supplies at a discount which ultimately allows them to sell their products at a lower cost than most of their competitors.&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
Before we present our model, it will be helpful to explain a few details in order to gain a better understanding in how our model works. Initially, our flag corporation can produce the first 20 flags in an order for $100.00. Any extraneous flags in that particular order will cost us an additional $7.00 per flag. From our above linear model, we can see that any additional extraneous flags actually cost more per unit when compared to the $5.00 per unit we were charged for placing an order of 20 flags. This fact is a bit disturbing because our supplier is punishing us for purchasing more than 20 flags! It&#039;s almost like our supplier does not want us to buy more from them. Because of this fact, our initial figures need to be changed to illustrate the economy of scale phenomena. Rather than punishing us, our supplier makes the following changes to their pricing to encourage bulk purchases. The following changes are illustrated in our chart listed below and one can see that as our production level increases, our cost per unit actually decreases.&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
Here is a following chart that demonstrates the economy of scale phenomena: [[File:110 jura graph.xlsx]]. You can see our formulas by clicking each respective cell in the chart. Feel free to play with the inputs as well. The inputs are shaded brown and the chart will automatically update according to your inputs.&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
One key note that we must address is that the marginal cost per unit should be cheaper than the production level cost per unit because marginal cost is the extra amount we have to pay past our production level. Since we are Jura Corporation, it is honourable for our supplier to reward us with a discount if we buy in bulk! Also, the unit price cannot keep on getting cheaper. Even though Jura Corporation is purchasing in bulk, we will eventually reach a limit where the discounts will remain stable.&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
&amp;lt;i&amp;gt;I&#039;ll need to manually graph this out and scan it in.&amp;lt;/i&amp;gt;&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&amp;lt;b&amp;gt;&amp;lt;i&amp;gt;&lt;br /&gt;
Other interesting properties that you can think of and create a model for. &lt;br /&gt;
&amp;lt;/b&amp;gt;&amp;lt;/i&amp;gt;&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
Solution goes here.&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
== Discussion ==&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
Hello, team Jura. This is Adam, your  new teammate. As you may be aware, there is a team question that is posted. Please take a look and be familiar with the question. We are to write a comprehensive essay on the given problem. To complete this assignment, I propose that we each pick a few points, study those points and write a paragraph on them (ex. Someone can describe the model and find out the cost of 150 units etc.) We&#039;ll then combine our information and I&#039;ll volunteer to write up a good copy.&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
I have already finished the first 4 points &lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
Describe your model.&lt;br /&gt;
What does your model predict for a production of 150 items?&lt;br /&gt;
According yo your model, what happens to the average cost per item as production levels increase?&lt;br /&gt;
Finally, find some other models (not necessarily linear) for which you get other behaviours such as:&lt;br /&gt;
The average cost remains constant as production increases.&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
I&#039;ll leave up to you guys to the rest. Just pick a point or two to study. &lt;br /&gt;
Remember, there is a group evaluation at the end. Please participate so I can give each of you guys 100% in participation marks at the end.&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
Alright guys, lets start this year with a blast!&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
-Adam Nguyen&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
I will do the next two points from where Adam left off tonight - that leaves the last 2 points.&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
-Christa Bicego&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
Since there are two points left, I&#039;ll work on the Economies of Scale model.&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
-Matthew&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
Alright, I have the framework for our economy of scale question. I think it&#039;s correct, but any feedback on it would be appreciated. If everything looks alright, I&#039;ll finish the graph and scan it in. If you need to contact me, feel free to email me. I just posted my contact information on our Wiki.&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
-Matthew&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
Just did some formatting on our page to give it some structure. If you&#039;re unfamiliar with posting on the Wiki, I&#039;ve templated where you can copy and paste your responses into to make things a bit easier.&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
-Matthew&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;/div&gt;</summary>
		<author><name>AdamsNguyen</name></author>
	</entry>
	<entry>
		<id>https://wiki.ubc.ca/index.php?title=Course:MATH110/Archive/2010-2011/003/Teams/Jura/Homework/11_Part3&amp;diff=70819</id>
		<title>Course:MATH110/Archive/2010-2011/003/Teams/Jura/Homework/11 Part3</title>
		<link rel="alternate" type="text/html" href="https://wiki.ubc.ca/index.php?title=Course:MATH110/Archive/2010-2011/003/Teams/Jura/Homework/11_Part3&amp;diff=70819"/>
		<updated>2011-01-19T06:20:34Z</updated>

		<summary type="html">&lt;p&gt;AdamsNguyen: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;&amp;lt;p&amp;gt;&amp;lt;b&amp;gt;&amp;lt;i&amp;gt;&lt;br /&gt;
Write a linear model to predict the cost of producing flags of your team&#039;s Canton under the assumptions that the marginal cost is $7 per unit and that at the current production level of 20 items, the cost is $100.&lt;br /&gt;
&amp;lt;/b&amp;gt;&amp;lt;/i&amp;gt;&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
The following linear equation is a model to predict the cost of producing flags of a Canton under the assumption that the marginal cost is $7 per unit and that at the current production level of 20 items, the cost is $100. C(F) = 7F – 40.&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&amp;lt;b&amp;gt;&amp;lt;i&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Describe your model.&lt;br /&gt;
&amp;lt;/b&amp;gt;&amp;lt;/i&amp;gt;&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
[[File:plot123.gif]]&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&amp;lt;b&amp;gt;&amp;lt;i&amp;gt;&lt;br /&gt;
What does your model predict for a production of 150 items?&lt;br /&gt;
&amp;lt;/b&amp;gt;&amp;lt;/i&amp;gt;&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
This model predicts that at the production of 150 items, the cost $1010.&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&amp;lt;b&amp;gt;&amp;lt;i&amp;gt;&lt;br /&gt;
According to your model, what happens to the average cost per item as production levels increase?&lt;br /&gt;
&amp;lt;/b&amp;gt;&amp;lt;/i&amp;gt;&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
According to this model, the average cost per item will increase as production levels increase.&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&amp;lt;b&amp;gt;&amp;lt;i&amp;gt;&lt;br /&gt;
The average cost remains constant as production increases.&lt;br /&gt;
&amp;lt;/b&amp;gt;&amp;lt;/i&amp;gt;&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
A model with this attribute intersects the origin and has a constant slope. Therefore an equation of this type of model would look like:&amp;lt;br&amp;gt;&lt;br /&gt;
C(F) = XF&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
For example:&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
C(F) = 7F&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
C(F) = F&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&amp;lt;b&amp;gt;&amp;lt;i&amp;gt;&lt;br /&gt;
The average cost diminishes as production increases (-,+)&lt;br /&gt;
&amp;lt;/b&amp;gt;&amp;lt;/i&amp;gt;&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Average Cost= total cost/ production&amp;lt;br /&amp;gt;&lt;br /&gt;
&amp;lt;br /&amp;gt;&lt;br /&gt;
A new model example: The marginal cost of a 3D t.v. is $400 dollars per unit at current production of 10 items, the cost is $5000 dollars.&amp;lt;br /&amp;gt;&lt;br /&gt;
C(10)= 400(10)+ x&amp;lt;br /&amp;gt;&lt;br /&gt;
C(10) = 4000 + x&amp;lt;br /&amp;gt;&lt;br /&gt;
5000- 4000 = x&amp;lt;br /&amp;gt;&lt;br /&gt;
x= 1000&amp;lt;br /&amp;gt;&lt;br /&gt;
&amp;lt;br /&amp;gt;&lt;br /&gt;
C(F)= 400F + 1000&amp;lt;br /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Average Cost= total cost/ production&amp;lt;br /&amp;gt;&lt;br /&gt;
C(10)= 400(10) +1000 = 5000/10 = 500&amp;lt;br /&amp;gt;&lt;br /&gt;
C(20) = 400(20) +1000 = 9000/20 = 450&amp;lt;br /&amp;gt;&lt;br /&gt;
C(25)= 400(25) +1000 = 11000/ 25 = 440&amp;lt;br /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Conclusion: the data shows that the average cost becomes smaller as production increases&amp;lt;br /&amp;gt;&lt;br /&gt;
AvgC becomes smaller when Production increases&amp;lt;br /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&amp;lt;b&amp;gt;&amp;lt;i&amp;gt;&lt;br /&gt;
The average cost increases as production increases.&lt;br /&gt;
&amp;lt;/b&amp;gt;&amp;lt;/i&amp;gt;&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
Average cost becomes larger when Production becomes larger ( +,+)&amp;lt;br /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Average Cost= total cost/ production&amp;lt;br /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
 new model: The marginal cost of a pair of runners is $8 dollars per unit and that at the current production level of 50 items, the cost is $200 dollars &amp;lt;br /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
C(F)= 8F - 200&amp;lt;br /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The average cost is getting larger when production becomes larger shown by substituting larger production quantities into the function for F.&amp;lt;br /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
C(50)= 8(50)- 200 = 200&amp;lt;br /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
C(51)= 8(51)- 200 = 208&amp;lt;br /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Average Cost= total cost/ production&amp;lt;br /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
C(50)= 200/ 50 = 4&amp;lt;br /&amp;gt;&lt;br /&gt;
C(51)= 208/51 = 4.07&amp;lt;br /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
This represents that the function C(F) is increasing and on a graph shows that as one moves up the function both production and average costs are increasing.&amp;lt;br /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&amp;lt;b&amp;gt;&amp;lt;i&amp;gt;&lt;br /&gt;
You obtain an economy of scale. This means that starting at some specific production level, the marginal cost is always less than the average cost.&lt;br /&gt;
&amp;lt;/b&amp;gt;&amp;lt;/i&amp;gt;&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
Before we begin to describe our model for an economy of scale, it will be helpful to understand exactly what an economy of scale is. With this term being somewhat novel to our group, our research instructed us that economies of scale describes the decreased per unit cost as the number of units of production increases. Basically, it means that when our flag corporation produces a certain amount of flags, that our corporation will realize a reduction in the per unit cost of our flags as our corporation&#039;s production level increases.&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
We can think of this definition contextually by examining Walmart. Walmart is a good example at a corporation that exploits the notion of economies of scale because it purchases its supplies in bulk. This mass purchasing of supplies allows Walmart to buy these supplies at a discount which ultimately allows them to sell their products at a lower cost than most of their competitors.&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
Before we present our model, it will be helpful to explain a few details in order to gain a better understanding in how our model works. Initially, our flag corporation can produce the first 20 flags in an order for $100.00. Any extraneous flags in that particular order will cost us an additional $7.00 per flag. From our above linear model, we can see that any additional extraneous flags actually cost more per unit when compared to the $5.00 per unit we were charged for placing an order of 20 flags. This fact is a bit disturbing because our supplier is punishing us for purchasing more than 20 flags! It&#039;s almost like our supplier does not want us to buy more from them. Because of this fact, our initial figures need to be changed to illustrate the economy of scale phenomena. Rather than punishing us, our supplier makes the following changes to their pricing to encourage bulk purchases. The following changes are illustrated in our chart listed below and one can see that as our production level increases, our cost per unit actually decreases.&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
Here is a following chart that demonstrates the economy of scale phenomena: [[File:110 jura graph.xlsx]]. You can see our formulas by clicking each respective cell in the chart. Feel free to play with the inputs as well. The inputs are shaded brown and the chart will automatically update according to your inputs.&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
One key note that we must address is that the marginal cost per unit should be cheaper than the production level cost per unit because marginal cost is the extra amount we have to pay past our production level. Since we are Jura Corporation, it is honourable for our supplier to reward us with a discount if we buy in bulk! Also, the unit price cannot keep on getting cheaper. Even though Jura Corporation is purchasing in bulk, we will eventually reach a limit where the discounts will remain stable.&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
&amp;lt;i&amp;gt;I&#039;ll need to manually graph this out and scan it in.&amp;lt;/i&amp;gt;&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&amp;lt;b&amp;gt;&amp;lt;i&amp;gt;&lt;br /&gt;
Other interesting properties that you can think of and create a model for. &lt;br /&gt;
&amp;lt;/b&amp;gt;&amp;lt;/i&amp;gt;&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
Solution goes here.&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
== Discussion ==&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
Hello, team Jura. This is Adam, your  new teammate. As you may be aware, there is a team question that is posted. Please take a look and be familiar with the question. We are to write a comprehensive essay on the given problem. To complete this assignment, I propose that we each pick a few points, study those points and write a paragraph on them (ex. Someone can describe the model and find out the cost of 150 units etc.) We&#039;ll then combine our information and I&#039;ll volunteer to write up a good copy.&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
I have already finished the first 4 points &lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
Describe your model.&lt;br /&gt;
What does your model predict for a production of 150 items?&lt;br /&gt;
According yo your model, what happens to the average cost per item as production levels increase?&lt;br /&gt;
Finally, find some other models (not necessarily linear) for which you get other behaviours such as:&lt;br /&gt;
The average cost remains constant as production increases.&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
I&#039;ll leave up to you guys to the rest. Just pick a point or two to study. &lt;br /&gt;
Remember, there is a group evaluation at the end. Please participate so I can give each of you guys 100% in participation marks at the end.&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
Alright guys, lets start this year with a blast!&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
-Adam Nguyen&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
I will do the next two points from where Adam left off tonight - that leaves the last 2 points.&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
-Christa Bicego&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
Since there are two points left, I&#039;ll work on the Economies of Scale model.&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
-Matthew&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
Alright, I have the framework for our economy of scale question. I think it&#039;s correct, but any feedback on it would be appreciated. If everything looks alright, I&#039;ll finish the graph and scan it in. If you need to contact me, feel free to email me. I just posted my contact information on our Wiki.&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
-Matthew&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
Just did some formatting on our page to give it some structure. If you&#039;re unfamiliar with posting on the Wiki, I&#039;ve templated where you can copy and paste your responses into to make things a bit easier.&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
-Matthew&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;/div&gt;</summary>
		<author><name>AdamsNguyen</name></author>
	</entry>
	<entry>
		<id>https://wiki.ubc.ca/index.php?title=Course:MATH110/Archive/2010-2011/003/Teams/Jura/Homework/11_Part3&amp;diff=70818</id>
		<title>Course:MATH110/Archive/2010-2011/003/Teams/Jura/Homework/11 Part3</title>
		<link rel="alternate" type="text/html" href="https://wiki.ubc.ca/index.php?title=Course:MATH110/Archive/2010-2011/003/Teams/Jura/Homework/11_Part3&amp;diff=70818"/>
		<updated>2011-01-19T06:15:46Z</updated>

		<summary type="html">&lt;p&gt;AdamsNguyen: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;&amp;lt;p&amp;gt;&amp;lt;b&amp;gt;&amp;lt;i&amp;gt;&lt;br /&gt;
Write a linear model to predict the cost of producing flags of your team&#039;s Canton under the assumptions that the marginal cost is $7 per unit and that at the current production level of 20 items, the cost is $100.&lt;br /&gt;
&amp;lt;/b&amp;gt;&amp;lt;/i&amp;gt;&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
The following linear equation is a model to predict the cost of producing flags of a Canton under the assumption that the marginal cost is $7 per unit and that at the current production level of 20 items, the cost is $100. C(F) = 7F – 40.&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&amp;lt;b&amp;gt;&amp;lt;i&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Describe your model.&lt;br /&gt;
&amp;lt;/b&amp;gt;&amp;lt;/i&amp;gt;&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
[[File:plot123.gif]]&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&amp;lt;b&amp;gt;&amp;lt;i&amp;gt;&lt;br /&gt;
What does your model predict for a production of 150 items?&lt;br /&gt;
&amp;lt;/b&amp;gt;&amp;lt;/i&amp;gt;&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
This model predicts that at the production of 150 items, the cost $1010.&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&amp;lt;b&amp;gt;&amp;lt;i&amp;gt;&lt;br /&gt;
According to your model, what happens to the average cost per item as production levels increase?&lt;br /&gt;
&amp;lt;/b&amp;gt;&amp;lt;/i&amp;gt;&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
According to this model, the average cost per item will increase as production levels increase.&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&amp;lt;b&amp;gt;&amp;lt;i&amp;gt;&lt;br /&gt;
The average cost remains constant as production increases.&lt;br /&gt;
&amp;lt;/b&amp;gt;&amp;lt;/i&amp;gt;&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
C (F) = 7F&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
C (F) = F&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&amp;lt;b&amp;gt;&amp;lt;i&amp;gt;&lt;br /&gt;
The average cost diminishes as production increases (-,+)&lt;br /&gt;
&amp;lt;/b&amp;gt;&amp;lt;/i&amp;gt;&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Average Cost= total cost/ production&amp;lt;br /&amp;gt;&lt;br /&gt;
&amp;lt;br /&amp;gt;&lt;br /&gt;
A new model example: The marginal cost of a 3D t.v. is $400 dollars per unit at current production of 10 items, the cost is $5000 dollars.&amp;lt;br /&amp;gt;&lt;br /&gt;
C(10)= 400(10)+ x&amp;lt;br /&amp;gt;&lt;br /&gt;
C(10) = 4000 + x&amp;lt;br /&amp;gt;&lt;br /&gt;
5000- 4000 = x&amp;lt;br /&amp;gt;&lt;br /&gt;
x= 1000&amp;lt;br /&amp;gt;&lt;br /&gt;
&amp;lt;br /&amp;gt;&lt;br /&gt;
C(F)= 400F + 1000&amp;lt;br /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Average Cost= total cost/ production&amp;lt;br /&amp;gt;&lt;br /&gt;
C(10)= 400(10) +1000 = 5000/10 = 500&amp;lt;br /&amp;gt;&lt;br /&gt;
C(20) = 400(20) +1000 = 9000/20 = 450&amp;lt;br /&amp;gt;&lt;br /&gt;
C(25)= 400(25) +1000 = 11000/ 25 = 440&amp;lt;br /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Conclusion: the data shows that the average cost becomes smaller as production increases&amp;lt;br /&amp;gt;&lt;br /&gt;
AvgC becomes smaller when Production increases&amp;lt;br /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&amp;lt;b&amp;gt;&amp;lt;i&amp;gt;&lt;br /&gt;
The average cost increases as production increases.&lt;br /&gt;
&amp;lt;/b&amp;gt;&amp;lt;/i&amp;gt;&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
Average cost becomes larger when Production becomes larger ( +,+)&amp;lt;br /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Average Cost= total cost/ production&amp;lt;br /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
 new model: The marginal cost of a pair of runners is $8 dollars per unit and that at the current production level of 50 items, the cost is $200 dollars &amp;lt;br /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
C(F)= 8F - 200&amp;lt;br /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The average cost is getting larger when production becomes larger shown by substituting larger production quantities into the function for F.&amp;lt;br /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
C(50)= 8(50)- 200 = 200&amp;lt;br /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
C(51)= 8(51)- 200 = 208&amp;lt;br /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Average Cost= total cost/ production&amp;lt;br /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
C(50)= 200/ 50 = 4&amp;lt;br /&amp;gt;&lt;br /&gt;
C(51)= 208/51 = 4.07&amp;lt;br /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
This represents that the function C(F) is increasing and on a graph shows that as one moves up the function both production and average costs are increasing.&amp;lt;br /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&amp;lt;b&amp;gt;&amp;lt;i&amp;gt;&lt;br /&gt;
You obtain an economy of scale. This means that starting at some specific production level, the marginal cost is always less than the average cost.&lt;br /&gt;
&amp;lt;/b&amp;gt;&amp;lt;/i&amp;gt;&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
Before we begin to describe our model for an economy of scale, it will be helpful to understand exactly what an economy of scale is. With this term being somewhat novel to our group, our research instructed us that economies of scale describes the decreased per unit cost as the number of units of production increases. Basically, it means that when our flag corporation produces a certain amount of flags, that our corporation will realize a reduction in the per unit cost of our flags as our corporation&#039;s production level increases.&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
We can think of this definition contextually by examining Walmart. Walmart is a good example at a corporation that exploits the notion of economies of scale because it purchases its supplies in bulk. This mass purchasing of supplies allows Walmart to buy these supplies at a discount which ultimately allows them to sell their products at a lower cost than most of their competitors.&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
Before we present our model, it will be helpful to explain a few details in order to gain a better understanding in how our model works. Initially, our flag corporation can produce the first 20 flags in an order for $100.00. Any extraneous flags in that particular order will cost us an additional $7.00 per flag. From our above linear model, we can see that any additional extraneous flags actually cost more per unit when compared to the $5.00 per unit we were charged for placing an order of 20 flags. This fact is a bit disturbing because our supplier is punishing us for purchasing more than 20 flags! It&#039;s almost like our supplier does not want us to buy more from them. Because of this fact, our initial figures need to be changed to illustrate the economy of scale phenomena. Rather than punishing us, our supplier makes the following changes to their pricing to encourage bulk purchases. The following changes are illustrated in our chart listed below and one can see that as our production level increases, our cost per unit actually decreases.&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
Here is a following chart that demonstrates the economy of scale phenomena: [[File:110 jura graph.xlsx]]. You can see our formulas by clicking each respective cell in the chart. Feel free to play with the inputs as well. The inputs are shaded brown and the chart will automatically update according to your inputs.&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
One key note that we must address is that the marginal cost per unit should be cheaper than the production level cost per unit because marginal cost is the extra amount we have to pay past our production level. Since we are Jura Corporation, it is honourable for our supplier to reward us with a discount if we buy in bulk! Also, the unit price cannot keep on getting cheaper. Even though Jura Corporation is purchasing in bulk, we will eventually reach a limit where the discounts will remain stable.&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
&amp;lt;i&amp;gt;I&#039;ll need to manually graph this out and scan it in.&amp;lt;/i&amp;gt;&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&amp;lt;b&amp;gt;&amp;lt;i&amp;gt;&lt;br /&gt;
Other interesting properties that you can think of and create a model for. &lt;br /&gt;
&amp;lt;/b&amp;gt;&amp;lt;/i&amp;gt;&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
Solution goes here.&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
== Discussion ==&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
Hello, team Jura. This is Adam, your  new teammate. As you may be aware, there is a team question that is posted. Please take a look and be familiar with the question. We are to write a comprehensive essay on the given problem. To complete this assignment, I propose that we each pick a few points, study those points and write a paragraph on them (ex. Someone can describe the model and find out the cost of 150 units etc.) We&#039;ll then combine our information and I&#039;ll volunteer to write up a good copy.&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
I have already finished the first 4 points &lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
Describe your model.&lt;br /&gt;
What does your model predict for a production of 150 items?&lt;br /&gt;
According yo your model, what happens to the average cost per item as production levels increase?&lt;br /&gt;
Finally, find some other models (not necessarily linear) for which you get other behaviours such as:&lt;br /&gt;
The average cost remains constant as production increases.&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
I&#039;ll leave up to you guys to the rest. Just pick a point or two to study. &lt;br /&gt;
Remember, there is a group evaluation at the end. Please participate so I can give each of you guys 100% in participation marks at the end.&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
Alright guys, lets start this year with a blast!&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
-Adam Nguyen&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
I will do the next two points from where Adam left off tonight - that leaves the last 2 points.&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
-Christa Bicego&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
Since there are two points left, I&#039;ll work on the Economies of Scale model.&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
-Matthew&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
Alright, I have the framework for our economy of scale question. I think it&#039;s correct, but any feedback on it would be appreciated. If everything looks alright, I&#039;ll finish the graph and scan it in. If you need to contact me, feel free to email me. I just posted my contact information on our Wiki.&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
-Matthew&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
Just did some formatting on our page to give it some structure. If you&#039;re unfamiliar with posting on the Wiki, I&#039;ve templated where you can copy and paste your responses into to make things a bit easier.&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
-Matthew&lt;br /&gt;
&amp;lt;/p&amp;gt;&lt;/div&gt;</summary>
		<author><name>AdamsNguyen</name></author>
	</entry>
	<entry>
		<id>https://wiki.ubc.ca/index.php?title=Course:MATH110/Archive/2010-2011/003/Teams/Jura&amp;diff=70170</id>
		<title>Course:MATH110/Archive/2010-2011/003/Teams/Jura</title>
		<link rel="alternate" type="text/html" href="https://wiki.ubc.ca/index.php?title=Course:MATH110/Archive/2010-2011/003/Teams/Jura&amp;diff=70170"/>
		<updated>2011-01-17T21:00:57Z</updated>

		<summary type="html">&lt;p&gt;AdamsNguyen: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;{{Infobox MATH110 Teams&lt;br /&gt;
| team name = Jura&lt;br /&gt;
| member 1 = Adam Nguyen, adam@premierwestmma.com&lt;br /&gt;
| member 2 = Christa Bicego&lt;br /&gt;
| member 3 = Matthew Hsu&lt;br /&gt;
| member 4 = Shamilla Birring&lt;br /&gt;
}}&lt;br /&gt;
In workshop L.&lt;br /&gt;
&lt;br /&gt;
== Team Question 1 ==&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The following linear equation is a model to predict the cost of producing flags of a Canton under the assumption that the marginal cost is $7 per unit and that at the current production level of 20 items, the cost is $100.:&lt;br /&gt;
C(F) = 7F – 40&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
[[File:plot123.gif]]&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
This model predicts that at the production of 150 items, the cost $1010.&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
According to this model, the average cost per item will increase as production levels increase&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
===Models for which the average cost remains constant as production increases:===&lt;br /&gt;
C (F) = 7F&lt;br /&gt;
C (F) = F&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
== Discussion ==&lt;br /&gt;
Hello, team Jura. This is Adam, your  new teammate. As you may be aware, there is a team question that is posted. Please take a look and be familiar with the question. We are to write a comprehensive essay on the given problem. To complete this assignment, I propose that we each pick a few points, study those points and write a paragraph on them (ex. Someone can describe the model and find out the cost of 150 units etc.) We&#039;ll then combine our information and I&#039;ll volunteer to write up a good copy.&lt;br /&gt;
&lt;br /&gt;
I have already finished the first 4 points &lt;br /&gt;
&lt;br /&gt;
Describe your model.&lt;br /&gt;
What does your model predict for a production of 150 items?&lt;br /&gt;
According yo your model, what happens to the average cost per item as production levels increase?&lt;br /&gt;
Finally, find some other models (not necessarily linear) for which you get other behaviours such as:&lt;br /&gt;
The average cost remains constant as production increases.&lt;br /&gt;
&lt;br /&gt;
I&#039;ll leave up to you guys to the rest. Just pick a point or two to study. &lt;br /&gt;
Remember, there is a group evaluation at the end. Please participate so I can give each of you guys 100% in participation marks at the end.&lt;br /&gt;
&lt;br /&gt;
Alright guys, lets start this year with a blast!&lt;br /&gt;
&lt;br /&gt;
-Adam Nguyen&lt;br /&gt;
&lt;br /&gt;
I will do the next two points from where Adam left off tonight - that leaves the last 2 points&lt;br /&gt;
Christa Bicego&lt;/div&gt;</summary>
		<author><name>AdamsNguyen</name></author>
	</entry>
	<entry>
		<id>https://wiki.ubc.ca/index.php?title=Course:MATH110/Archive/2010-2011/003/Teams/Jura&amp;diff=70081</id>
		<title>Course:MATH110/Archive/2010-2011/003/Teams/Jura</title>
		<link rel="alternate" type="text/html" href="https://wiki.ubc.ca/index.php?title=Course:MATH110/Archive/2010-2011/003/Teams/Jura&amp;diff=70081"/>
		<updated>2011-01-17T09:02:30Z</updated>

		<summary type="html">&lt;p&gt;AdamsNguyen: /* Team Question 1 */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;{{Infobox MATH110 Teams&lt;br /&gt;
| team name = Jura&lt;br /&gt;
| member 1 = Adam Nguyen&lt;br /&gt;
| member 2 = Christa Bicego&lt;br /&gt;
| member 3 = Matthew Hsu&lt;br /&gt;
| member 4 = Shamilla Birring&lt;br /&gt;
}}&lt;br /&gt;
In workshop L.&lt;br /&gt;
&lt;br /&gt;
== Team Question 1 ==&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The following linear equation is a model to predict the cost of producing flags of a Canton under the assumption that the marginal cost is $7 per unit and that at the current production level of 20 items, the cost is $100.:&lt;br /&gt;
C(F) = 7F – 40&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
[[File:plot123.gif]]&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
This model predicts that at the production of 150 items, the cost $1010.&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
According to this model, the average cost per item will increase as production levels increase&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
===Models for which the average cost remains constant as production increases:===&lt;br /&gt;
C (F) = 7F&lt;br /&gt;
C (F) = F&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
== Discussion ==&lt;br /&gt;
Hello, team Jura. This is Adam, your  new teammate. As you may be aware, there is a team question that is posted. Please take a look and be familiar with the question. We are to write a comprehensive essay on the given problem. To complete this assignment, I propose that we each pick a few points, study those points and write a paragraph on them (ex. Someone can describe the model and find out the cost of 150 units etc.) We&#039;ll then combine our information and I&#039;ll volunteer to write up a good copy.&lt;br /&gt;
&lt;br /&gt;
I have already finished the first 4 points &lt;br /&gt;
&lt;br /&gt;
Describe your model.&lt;br /&gt;
What does your model predict for a production of 150 items?&lt;br /&gt;
According yo your model, what happens to the average cost per item as production levels increase?&lt;br /&gt;
Finally, find some other models (not necessarily linear) for which you get other behaviours such as:&lt;br /&gt;
The average cost remains constant as production increases.&lt;br /&gt;
&lt;br /&gt;
I&#039;ll leave up to you guys to the rest. Just pick a point or two to study. &lt;br /&gt;
Remember, there is a group evaluation at the end. Please participate so I can give each of you guys 100% in participation marks at the end.&lt;br /&gt;
&lt;br /&gt;
Alright guys, lets start this year with a blast!&lt;br /&gt;
&lt;br /&gt;
-Adam Nguyen&lt;br /&gt;
&lt;br /&gt;
I will do the next two points from where Adam left off tonight - that leaves the last 2 points&lt;br /&gt;
Christa Bicego&lt;/div&gt;</summary>
		<author><name>AdamsNguyen</name></author>
	</entry>
	<entry>
		<id>https://wiki.ubc.ca/index.php?title=Course:MATH110/Archive/2010-2011/003/Teams/Jura&amp;diff=70080</id>
		<title>Course:MATH110/Archive/2010-2011/003/Teams/Jura</title>
		<link rel="alternate" type="text/html" href="https://wiki.ubc.ca/index.php?title=Course:MATH110/Archive/2010-2011/003/Teams/Jura&amp;diff=70080"/>
		<updated>2011-01-17T09:02:05Z</updated>

		<summary type="html">&lt;p&gt;AdamsNguyen: /* Team Question 1 */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;{{Infobox MATH110 Teams&lt;br /&gt;
| team name = Jura&lt;br /&gt;
| member 1 = Adam Nguyen&lt;br /&gt;
| member 2 = Christa Bicego&lt;br /&gt;
| member 3 = Matthew Hsu&lt;br /&gt;
| member 4 = Shamilla Birring&lt;br /&gt;
}}&lt;br /&gt;
In workshop L.&lt;br /&gt;
&lt;br /&gt;
== Team Question 1 ==&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The following linear equation is a model to predict the cost of producing flags of a Canton under the assumption that the marginal cost is $7 per unit and that at the current production level of 20 items, the cost is $100.:&lt;br /&gt;
C(F) = 7F – 40&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
[[File:plot123.gif]]&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
This model predicts that at the production of 150 items, the cost $1010.&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
According to this model, the average cost per item will increase as production levels increase&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
===Models for which the average cost remains constant as production increases:===&lt;br /&gt;
C (F) = 7F&lt;br /&gt;
C (F) = F&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
== Discussion ==&lt;br /&gt;
Hello, team Jura. This is Adam, your  new teammate. As you may be aware, there is a team question that is posted. Please take a look and be familiar with the question. We are to write a comprehensive essay on the given problem. To complete this assignment, I propose that we each pick a few points, study those points and write a paragraph on them (ex. Someone can describe the model and find out the cost of 150 units etc.) We&#039;ll then combine our information and I&#039;ll volunteer to write up a good copy.&lt;br /&gt;
&lt;br /&gt;
I have already finished the first 4 points &lt;br /&gt;
&lt;br /&gt;
Describe your model.&lt;br /&gt;
What does your model predict for a production of 150 items?&lt;br /&gt;
According yo your model, what happens to the average cost per item as production levels increase?&lt;br /&gt;
Finally, find some other models (not necessarily linear) for which you get other behaviours such as:&lt;br /&gt;
The average cost remains constant as production increases.&lt;br /&gt;
&lt;br /&gt;
I&#039;ll leave up to you guys to the rest. Just pick a point or two to study. &lt;br /&gt;
Remember, there is a group evaluation at the end. Please participate so I can give each of you guys 100% in participation marks at the end.&lt;br /&gt;
&lt;br /&gt;
Alright guys, lets start this year with a blast!&lt;br /&gt;
&lt;br /&gt;
-Adam Nguyen&lt;br /&gt;
&lt;br /&gt;
I will do the next two points from where Adam left off tonight - that leaves the last 2 points&lt;br /&gt;
Christa Bicego&lt;/div&gt;</summary>
		<author><name>AdamsNguyen</name></author>
	</entry>
	<entry>
		<id>https://wiki.ubc.ca/index.php?title=Course:MATH110/Archive/2010-2011/003/Teams/Jura&amp;diff=70079</id>
		<title>Course:MATH110/Archive/2010-2011/003/Teams/Jura</title>
		<link rel="alternate" type="text/html" href="https://wiki.ubc.ca/index.php?title=Course:MATH110/Archive/2010-2011/003/Teams/Jura&amp;diff=70079"/>
		<updated>2011-01-17T09:01:30Z</updated>

		<summary type="html">&lt;p&gt;AdamsNguyen: /* Team Question 1 */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;{{Infobox MATH110 Teams&lt;br /&gt;
| team name = Jura&lt;br /&gt;
| member 1 = Adam Nguyen&lt;br /&gt;
| member 2 = Christa Bicego&lt;br /&gt;
| member 3 = Matthew Hsu&lt;br /&gt;
| member 4 = Shamilla Birring&lt;br /&gt;
}}&lt;br /&gt;
In workshop L.&lt;br /&gt;
&lt;br /&gt;
== Team Question 1 ==&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The following linear equation is a model to predict the cost of producing flags of a Canton under the assumption that the marginal cost is $7 per unit and that at the current production level of 20 items, the cost is $100.:&lt;br /&gt;
C(F) = 7F – 40&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
[[File:plot123.gif]]&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
This model predicts that at the production of 150 items, the cost $1010.&lt;br /&gt;
According to this model, the average cost per item will increase as production levels increase&lt;br /&gt;
Models for which the average cost remains constant as production increases:&lt;br /&gt;
C (F) = 7F&lt;br /&gt;
C (F) = F&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
== Discussion ==&lt;br /&gt;
Hello, team Jura. This is Adam, your  new teammate. As you may be aware, there is a team question that is posted. Please take a look and be familiar with the question. We are to write a comprehensive essay on the given problem. To complete this assignment, I propose that we each pick a few points, study those points and write a paragraph on them (ex. Someone can describe the model and find out the cost of 150 units etc.) We&#039;ll then combine our information and I&#039;ll volunteer to write up a good copy.&lt;br /&gt;
&lt;br /&gt;
I have already finished the first 4 points &lt;br /&gt;
&lt;br /&gt;
Describe your model.&lt;br /&gt;
What does your model predict for a production of 150 items?&lt;br /&gt;
According yo your model, what happens to the average cost per item as production levels increase?&lt;br /&gt;
Finally, find some other models (not necessarily linear) for which you get other behaviours such as:&lt;br /&gt;
The average cost remains constant as production increases.&lt;br /&gt;
&lt;br /&gt;
I&#039;ll leave up to you guys to the rest. Just pick a point or two to study. &lt;br /&gt;
Remember, there is a group evaluation at the end. Please participate so I can give each of you guys 100% in participation marks at the end.&lt;br /&gt;
&lt;br /&gt;
Alright guys, lets start this year with a blast!&lt;br /&gt;
&lt;br /&gt;
-Adam Nguyen&lt;br /&gt;
&lt;br /&gt;
I will do the next two points from where Adam left off tonight - that leaves the last 2 points&lt;br /&gt;
Christa Bicego&lt;/div&gt;</summary>
		<author><name>AdamsNguyen</name></author>
	</entry>
	<entry>
		<id>https://wiki.ubc.ca/index.php?title=File:Plot123.gif&amp;diff=70078</id>
		<title>File:Plot123.gif</title>
		<link rel="alternate" type="text/html" href="https://wiki.ubc.ca/index.php?title=File:Plot123.gif&amp;diff=70078"/>
		<updated>2011-01-17T09:00:38Z</updated>

		<summary type="html">&lt;p&gt;AdamsNguyen: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;&lt;/div&gt;</summary>
		<author><name>AdamsNguyen</name></author>
	</entry>
	<entry>
		<id>https://wiki.ubc.ca/index.php?title=Course:MATH110/Archive/2010-2011/003/Teams/Jura&amp;diff=70077</id>
		<title>Course:MATH110/Archive/2010-2011/003/Teams/Jura</title>
		<link rel="alternate" type="text/html" href="https://wiki.ubc.ca/index.php?title=Course:MATH110/Archive/2010-2011/003/Teams/Jura&amp;diff=70077"/>
		<updated>2011-01-17T09:00:04Z</updated>

		<summary type="html">&lt;p&gt;AdamsNguyen: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;{{Infobox MATH110 Teams&lt;br /&gt;
| team name = Jura&lt;br /&gt;
| member 1 = Adam Nguyen&lt;br /&gt;
| member 2 = Christa Bicego&lt;br /&gt;
| member 3 = Matthew Hsu&lt;br /&gt;
| member 4 = Shamilla Birring&lt;br /&gt;
}}&lt;br /&gt;
In workshop L.&lt;br /&gt;
&lt;br /&gt;
== Team Question 1 ==&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The following linear equation is a model to predict the cost of producing flags of a Canton under the assumption that the marginal cost is $7 per unit and that at the current production level of 20 items, the cost is $100.:&lt;br /&gt;
C(F) = 7F – 40&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
[[File:plot123.gif]]&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
This model predicts that at the production of 150 items, the cost $1010.&lt;br /&gt;
According to this model, the average cost per item will increase as production levels increase&lt;br /&gt;
Models for which the average cost remains constant as production increases:&lt;br /&gt;
C (F) = 7F&lt;br /&gt;
C (F) = F&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
== Discussion ==&lt;br /&gt;
Hello, team Jura. This is Adam, your  new teammate. As you may be aware, there is a team question that is posted. Please take a look and be familiar with the question. We are to write a comprehensive essay on the given problem. To complete this assignment, I propose that we each pick a few points, study those points and write a paragraph on them (ex. Someone can describe the model and find out the cost of 150 units etc.) We&#039;ll then combine our information and I&#039;ll volunteer to write up a good copy.&lt;br /&gt;
&lt;br /&gt;
I have already finished the first 4 points &lt;br /&gt;
&lt;br /&gt;
Describe your model.&lt;br /&gt;
What does your model predict for a production of 150 items?&lt;br /&gt;
According yo your model, what happens to the average cost per item as production levels increase?&lt;br /&gt;
Finally, find some other models (not necessarily linear) for which you get other behaviours such as:&lt;br /&gt;
The average cost remains constant as production increases.&lt;br /&gt;
&lt;br /&gt;
I&#039;ll leave up to you guys to the rest. Just pick a point or two to study. &lt;br /&gt;
Remember, there is a group evaluation at the end. Please participate so I can give each of you guys 100% in participation marks at the end.&lt;br /&gt;
&lt;br /&gt;
Alright guys, lets start this year with a blast!&lt;br /&gt;
&lt;br /&gt;
-Adam Nguyen&lt;br /&gt;
&lt;br /&gt;
I will do the next two points from where Adam left off tonight - that leaves the last 2 points&lt;br /&gt;
Christa Bicego&lt;/div&gt;</summary>
		<author><name>AdamsNguyen</name></author>
	</entry>
	<entry>
		<id>https://wiki.ubc.ca/index.php?title=Course:MATH110/Archive/2010-2011/003/Teams/Jura&amp;diff=70076</id>
		<title>Course:MATH110/Archive/2010-2011/003/Teams/Jura</title>
		<link rel="alternate" type="text/html" href="https://wiki.ubc.ca/index.php?title=Course:MATH110/Archive/2010-2011/003/Teams/Jura&amp;diff=70076"/>
		<updated>2011-01-17T08:58:48Z</updated>

		<summary type="html">&lt;p&gt;AdamsNguyen: /* Team Question 1 */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;{{Infobox MATH110 Teams&lt;br /&gt;
| team name = Jura&lt;br /&gt;
| member 1 = Adam Nguyen&lt;br /&gt;
| member 2 = Christa Bicego&lt;br /&gt;
| member 3 = Matthew Hsu&lt;br /&gt;
| member 4 = Shamilla Birring&lt;br /&gt;
}}&lt;br /&gt;
In workshop L.&lt;br /&gt;
&lt;br /&gt;
== Team Question 1 ==&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The following linear equation is a model to predict the cost of producing flags of a Canton under the assumption that the marginal cost is $7 per unit and that at the current production level of 20 items, the cost is $100.:&lt;br /&gt;
C(F) = 7F – 40&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
[[File:Example.jpg]]&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
This model predicts that at the production of 150 items, the cost $1010.&lt;br /&gt;
According to this model, the average cost per item will increase as production levels increase&lt;br /&gt;
Models for which the average cost remains constant as production increases:&lt;br /&gt;
C (F) = 7F&lt;br /&gt;
C (F) = F&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
== Discussion ==&lt;br /&gt;
Hello, team Jura. This is Adam, your  new teammate. As you may be aware, there is a team question that is posted. Please take a look and be familiar with the question. We are to write a comprehensive essay on the given problem. To complete this assignment, I propose that we each pick a few points, study those points and write a paragraph on them (ex. Someone can describe the model and find out the cost of 150 units etc.) We&#039;ll then combine our information and I&#039;ll volunteer to write up a good copy.&lt;br /&gt;
&lt;br /&gt;
I have already finished the first 4 points &lt;br /&gt;
&lt;br /&gt;
Describe your model.&lt;br /&gt;
What does your model predict for a production of 150 items?&lt;br /&gt;
According yo your model, what happens to the average cost per item as production levels increase?&lt;br /&gt;
Finally, find some other models (not necessarily linear) for which you get other behaviours such as:&lt;br /&gt;
The average cost remains constant as production increases.&lt;br /&gt;
&lt;br /&gt;
I&#039;ll leave up to you guys to the rest. Just pick a point or two to study. &lt;br /&gt;
Remember, there is a group evaluation at the end. Please participate so I can give each of you guys 100% in participation marks at the end.&lt;br /&gt;
&lt;br /&gt;
Alright guys, lets start this year with a blast!&lt;br /&gt;
&lt;br /&gt;
-Adam Nguyen&lt;br /&gt;
&lt;br /&gt;
I will do the next two points from where Adam left off tonight - that leaves the last 2 points&lt;br /&gt;
Christa Bicego&lt;/div&gt;</summary>
		<author><name>AdamsNguyen</name></author>
	</entry>
	<entry>
		<id>https://wiki.ubc.ca/index.php?title=Course:MATH110/Archive/2010-2011/003/Teams/Jura&amp;diff=70075</id>
		<title>Course:MATH110/Archive/2010-2011/003/Teams/Jura</title>
		<link rel="alternate" type="text/html" href="https://wiki.ubc.ca/index.php?title=Course:MATH110/Archive/2010-2011/003/Teams/Jura&amp;diff=70075"/>
		<updated>2011-01-17T08:57:56Z</updated>

		<summary type="html">&lt;p&gt;AdamsNguyen: /* Team Question 1 */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;{{Infobox MATH110 Teams&lt;br /&gt;
| team name = Jura&lt;br /&gt;
| member 1 = Adam Nguyen&lt;br /&gt;
| member 2 = Christa Bicego&lt;br /&gt;
| member 3 = Matthew Hsu&lt;br /&gt;
| member 4 = Shamilla Birring&lt;br /&gt;
}}&lt;br /&gt;
In workshop L.&lt;br /&gt;
&lt;br /&gt;
== Team Question 1 ==&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The following linear equation is a model to predict the cost of producing flags of a Canton under the assumption that the marginal cost is $7 per unit and that at the current production level of 20 items, the cost is $100.:&lt;br /&gt;
C(F) = 7F – 40&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&amp;lt;img src=&amp;quot;http://www3.wolframalpha.com/Calculate/MSP/MSP27519e1i2dbedadh7bi00001ga7beg09i1456i5?MSPStoreType=image/gif&amp;amp;s=45&amp;amp;w=300&amp;amp;h=182&amp;quot;/&amp;gt;&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
This model predicts that at the production of 150 items, the cost $1010.&lt;br /&gt;
According to this model, the average cost per item will increase as production levels increase&lt;br /&gt;
Models for which the average cost remains constant as production increases:&lt;br /&gt;
C (F) = 7F&lt;br /&gt;
C (F) = F&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
== Discussion ==&lt;br /&gt;
Hello, team Jura. This is Adam, your  new teammate. As you may be aware, there is a team question that is posted. Please take a look and be familiar with the question. We are to write a comprehensive essay on the given problem. To complete this assignment, I propose that we each pick a few points, study those points and write a paragraph on them (ex. Someone can describe the model and find out the cost of 150 units etc.) We&#039;ll then combine our information and I&#039;ll volunteer to write up a good copy.&lt;br /&gt;
&lt;br /&gt;
I have already finished the first 4 points &lt;br /&gt;
&lt;br /&gt;
Describe your model.&lt;br /&gt;
What does your model predict for a production of 150 items?&lt;br /&gt;
According yo your model, what happens to the average cost per item as production levels increase?&lt;br /&gt;
Finally, find some other models (not necessarily linear) for which you get other behaviours such as:&lt;br /&gt;
The average cost remains constant as production increases.&lt;br /&gt;
&lt;br /&gt;
I&#039;ll leave up to you guys to the rest. Just pick a point or two to study. &lt;br /&gt;
Remember, there is a group evaluation at the end. Please participate so I can give each of you guys 100% in participation marks at the end.&lt;br /&gt;
&lt;br /&gt;
Alright guys, lets start this year with a blast!&lt;br /&gt;
&lt;br /&gt;
-Adam Nguyen&lt;br /&gt;
&lt;br /&gt;
I will do the next two points from where Adam left off tonight - that leaves the last 2 points&lt;br /&gt;
Christa Bicego&lt;/div&gt;</summary>
		<author><name>AdamsNguyen</name></author>
	</entry>
	<entry>
		<id>https://wiki.ubc.ca/index.php?title=Course:MATH110/Archive/2010-2011/003/Teams/Jura&amp;diff=70074</id>
		<title>Course:MATH110/Archive/2010-2011/003/Teams/Jura</title>
		<link rel="alternate" type="text/html" href="https://wiki.ubc.ca/index.php?title=Course:MATH110/Archive/2010-2011/003/Teams/Jura&amp;diff=70074"/>
		<updated>2011-01-17T08:54:52Z</updated>

		<summary type="html">&lt;p&gt;AdamsNguyen: /* Team Question 1 */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;{{Infobox MATH110 Teams&lt;br /&gt;
| team name = Jura&lt;br /&gt;
| member 1 = Adam Nguyen&lt;br /&gt;
| member 2 = Christa Bicego&lt;br /&gt;
| member 3 = Matthew Hsu&lt;br /&gt;
| member 4 = Shamilla Birring&lt;br /&gt;
}}&lt;br /&gt;
In workshop L.&lt;br /&gt;
&lt;br /&gt;
== Team Question 1 ==&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The following linear equation is a model to predict the cost of producing flags of a Canton under the assumption that the marginal cost is $7 per unit and that at the current production level of 20 items, the cost is $100.:&lt;br /&gt;
C(F) = 7F – 40&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
[[File:http://www3.wolframalpha.com/Calculate/MSP/MSP27519e1i2dbedadh7bi00001ga7beg09i1456i5?MSPStoreType=image/gif&amp;amp;s=45&amp;amp;w=300&amp;amp;h=182]]&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
This model predicts that at the production of 150 items, the cost $1010.&lt;br /&gt;
According to this model, the average cost per item will increase as production levels increase&lt;br /&gt;
Models for which the average cost remains constant as production increases:&lt;br /&gt;
C (F) = 7F&lt;br /&gt;
C (F) = F&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
== Discussion ==&lt;br /&gt;
Hello, team Jura. This is Adam, your  new teammate. As you may be aware, there is a team question that is posted. Please take a look and be familiar with the question. We are to write a comprehensive essay on the given problem. To complete this assignment, I propose that we each pick a few points, study those points and write a paragraph on them (ex. Someone can describe the model and find out the cost of 150 units etc.) We&#039;ll then combine our information and I&#039;ll volunteer to write up a good copy.&lt;br /&gt;
&lt;br /&gt;
I have already finished the first 4 points &lt;br /&gt;
&lt;br /&gt;
Describe your model.&lt;br /&gt;
What does your model predict for a production of 150 items?&lt;br /&gt;
According yo your model, what happens to the average cost per item as production levels increase?&lt;br /&gt;
Finally, find some other models (not necessarily linear) for which you get other behaviours such as:&lt;br /&gt;
The average cost remains constant as production increases.&lt;br /&gt;
&lt;br /&gt;
I&#039;ll leave up to you guys to the rest. Just pick a point or two to study. &lt;br /&gt;
Remember, there is a group evaluation at the end. Please participate so I can give each of you guys 100% in participation marks at the end.&lt;br /&gt;
&lt;br /&gt;
Alright guys, lets start this year with a blast!&lt;br /&gt;
&lt;br /&gt;
-Adam Nguyen&lt;br /&gt;
&lt;br /&gt;
I will do the next two points from where Adam left off tonight - that leaves the last 2 points&lt;br /&gt;
Christa Bicego&lt;/div&gt;</summary>
		<author><name>AdamsNguyen</name></author>
	</entry>
	<entry>
		<id>https://wiki.ubc.ca/index.php?title=Course:MATH110/Archive/2010-2011/003/Teams/Jura&amp;diff=70073</id>
		<title>Course:MATH110/Archive/2010-2011/003/Teams/Jura</title>
		<link rel="alternate" type="text/html" href="https://wiki.ubc.ca/index.php?title=Course:MATH110/Archive/2010-2011/003/Teams/Jura&amp;diff=70073"/>
		<updated>2011-01-17T08:53:26Z</updated>

		<summary type="html">&lt;p&gt;AdamsNguyen: /* Team Question 1 */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;{{Infobox MATH110 Teams&lt;br /&gt;
| team name = Jura&lt;br /&gt;
| member 1 = Adam Nguyen&lt;br /&gt;
| member 2 = Christa Bicego&lt;br /&gt;
| member 3 = Matthew Hsu&lt;br /&gt;
| member 4 = Shamilla Birring&lt;br /&gt;
}}&lt;br /&gt;
In workshop L.&lt;br /&gt;
&lt;br /&gt;
== Team Question 1 ==&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The following linear equation is a model to predict the cost of producing flags of a Canton under the assumption that the marginal cost is $7 per unit and that at the current production level of 20 items, the cost is $100.:&lt;br /&gt;
C(F) = 7F – 40&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&amp;lt;img src=&amp;quot;http://www3.wolframalpha.com/Calculate/MSP/MSP27519e1i2dbedadh7bi00001ga7beg09i1456i5?MSPStoreType=image/gif&amp;amp;s=45&amp;amp;w=300&amp;amp;h=182&amp;quot;/&amp;gt; &lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
This model predicts that at the production of 150 items, the cost $1010.&lt;br /&gt;
According to this model, the average cost per item will increase as production levels increase&lt;br /&gt;
Models for which the average cost remains constant as production increases:&lt;br /&gt;
C (F) = 7F&lt;br /&gt;
C (F) = F&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
== Discussion ==&lt;br /&gt;
Hello, team Jura. This is Adam, your  new teammate. As you may be aware, there is a team question that is posted. Please take a look and be familiar with the question. We are to write a comprehensive essay on the given problem. To complete this assignment, I propose that we each pick a few points, study those points and write a paragraph on them (ex. Someone can describe the model and find out the cost of 150 units etc.) We&#039;ll then combine our information and I&#039;ll volunteer to write up a good copy.&lt;br /&gt;
&lt;br /&gt;
I have already finished the first 4 points &lt;br /&gt;
&lt;br /&gt;
Describe your model.&lt;br /&gt;
What does your model predict for a production of 150 items?&lt;br /&gt;
According yo your model, what happens to the average cost per item as production levels increase?&lt;br /&gt;
Finally, find some other models (not necessarily linear) for which you get other behaviours such as:&lt;br /&gt;
The average cost remains constant as production increases.&lt;br /&gt;
&lt;br /&gt;
I&#039;ll leave up to you guys to the rest. Just pick a point or two to study. &lt;br /&gt;
Remember, there is a group evaluation at the end. Please participate so I can give each of you guys 100% in participation marks at the end.&lt;br /&gt;
&lt;br /&gt;
Alright guys, lets start this year with a blast!&lt;br /&gt;
&lt;br /&gt;
-Adam Nguyen&lt;br /&gt;
&lt;br /&gt;
I will do the next two points from where Adam left off tonight - that leaves the last 2 points&lt;br /&gt;
Christa Bicego&lt;/div&gt;</summary>
		<author><name>AdamsNguyen</name></author>
	</entry>
	<entry>
		<id>https://wiki.ubc.ca/index.php?title=Course:MATH110/Archive/2010-2011/003/Teams/Jura&amp;diff=70072</id>
		<title>Course:MATH110/Archive/2010-2011/003/Teams/Jura</title>
		<link rel="alternate" type="text/html" href="https://wiki.ubc.ca/index.php?title=Course:MATH110/Archive/2010-2011/003/Teams/Jura&amp;diff=70072"/>
		<updated>2011-01-17T08:52:03Z</updated>

		<summary type="html">&lt;p&gt;AdamsNguyen: /* Team Question 1 */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;{{Infobox MATH110 Teams&lt;br /&gt;
| team name = Jura&lt;br /&gt;
| member 1 = Adam Nguyen&lt;br /&gt;
| member 2 = Christa Bicego&lt;br /&gt;
| member 3 = Matthew Hsu&lt;br /&gt;
| member 4 = Shamilla Birring&lt;br /&gt;
}}&lt;br /&gt;
In workshop L.&lt;br /&gt;
&lt;br /&gt;
== Team Question 1 ==&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The following linear equation is a model to predict the cost of producing flags of a Canton under the assumption that the marginal cost is $7 per unit and that at the current production level of 20 items, the cost is $100.:&lt;br /&gt;
C(F) = 7F – 40&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&amp;lt;img src=&amp;quot;http://www3.wolframalpha.com/Calculate/MSP/MSP27519e1i2dbedadh7bi00001ga7beg09i1456i5?MSPStoreType=image/gif&amp;amp;amp;s=45&amp;amp;amp;w=300&amp;amp;amp;h=182&amp;quot; alt=&amp;quot;&amp;quot; width=&amp;quot;300&amp;quot; height=&amp;quot;182&amp;quot;/&amp;gt;&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
This model predicts that at the production of 150 items, the cost $1010.&lt;br /&gt;
According to this model, the average cost per item will increase as production levels increase&lt;br /&gt;
Models for which the average cost remains constant as production increases:&lt;br /&gt;
C (F) = 7F&lt;br /&gt;
C (F) = F&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
== Discussion ==&lt;br /&gt;
Hello, team Jura. This is Adam, your  new teammate. As you may be aware, there is a team question that is posted. Please take a look and be familiar with the question. We are to write a comprehensive essay on the given problem. To complete this assignment, I propose that we each pick a few points, study those points and write a paragraph on them (ex. Someone can describe the model and find out the cost of 150 units etc.) We&#039;ll then combine our information and I&#039;ll volunteer to write up a good copy.&lt;br /&gt;
&lt;br /&gt;
I have already finished the first 4 points &lt;br /&gt;
&lt;br /&gt;
Describe your model.&lt;br /&gt;
What does your model predict for a production of 150 items?&lt;br /&gt;
According yo your model, what happens to the average cost per item as production levels increase?&lt;br /&gt;
Finally, find some other models (not necessarily linear) for which you get other behaviours such as:&lt;br /&gt;
The average cost remains constant as production increases.&lt;br /&gt;
&lt;br /&gt;
I&#039;ll leave up to you guys to the rest. Just pick a point or two to study. &lt;br /&gt;
Remember, there is a group evaluation at the end. Please participate so I can give each of you guys 100% in participation marks at the end.&lt;br /&gt;
&lt;br /&gt;
Alright guys, lets start this year with a blast!&lt;br /&gt;
&lt;br /&gt;
-Adam Nguyen&lt;br /&gt;
&lt;br /&gt;
I will do the next two points from where Adam left off tonight - that leaves the last 2 points&lt;br /&gt;
Christa Bicego&lt;/div&gt;</summary>
		<author><name>AdamsNguyen</name></author>
	</entry>
	<entry>
		<id>https://wiki.ubc.ca/index.php?title=Course:MATH110/Archive/2010-2011/003/Teams/Jura&amp;diff=70071</id>
		<title>Course:MATH110/Archive/2010-2011/003/Teams/Jura</title>
		<link rel="alternate" type="text/html" href="https://wiki.ubc.ca/index.php?title=Course:MATH110/Archive/2010-2011/003/Teams/Jura&amp;diff=70071"/>
		<updated>2011-01-17T08:51:16Z</updated>

		<summary type="html">&lt;p&gt;AdamsNguyen: /* Team Question 1 */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;{{Infobox MATH110 Teams&lt;br /&gt;
| team name = Jura&lt;br /&gt;
| member 1 = Adam Nguyen&lt;br /&gt;
| member 2 = Christa Bicego&lt;br /&gt;
| member 3 = Matthew Hsu&lt;br /&gt;
| member 4 = Shamilla Birring&lt;br /&gt;
}}&lt;br /&gt;
In workshop L.&lt;br /&gt;
&lt;br /&gt;
== Team Question 1 ==&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The following linear equation is a model to predict the cost of producing flags of a Canton under the assumption that the marginal cost is $7 per unit and that at the current production level of 20 items, the cost is $100.:&lt;br /&gt;
C(F) = 7F – 40&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&amp;lt;img class=&amp;quot;alignnone&amp;quot; src=&amp;quot;http://www3.wolframalpha.com/Calculate/MSP/MSP27519e1i2dbedadh7bi00001ga7beg09i1456i5?MSPStoreType=image/gif&amp;amp;amp;s=45&amp;amp;amp;w=300&amp;amp;amp;h=182&amp;quot; alt=&amp;quot;&amp;quot; width=&amp;quot;300&amp;quot; height=&amp;quot;182&amp;quot; /&amp;gt;&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
This model predicts that at the production of 150 items, the cost $1010.&lt;br /&gt;
According to this model, the average cost per item will increase as production levels increase&lt;br /&gt;
Models for which the average cost remains constant as production increases:&lt;br /&gt;
C (F) = 7F&lt;br /&gt;
C (F) = F&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
== Discussion ==&lt;br /&gt;
Hello, team Jura. This is Adam, your  new teammate. As you may be aware, there is a team question that is posted. Please take a look and be familiar with the question. We are to write a comprehensive essay on the given problem. To complete this assignment, I propose that we each pick a few points, study those points and write a paragraph on them (ex. Someone can describe the model and find out the cost of 150 units etc.) We&#039;ll then combine our information and I&#039;ll volunteer to write up a good copy.&lt;br /&gt;
&lt;br /&gt;
I have already finished the first 4 points &lt;br /&gt;
&lt;br /&gt;
Describe your model.&lt;br /&gt;
What does your model predict for a production of 150 items?&lt;br /&gt;
According yo your model, what happens to the average cost per item as production levels increase?&lt;br /&gt;
Finally, find some other models (not necessarily linear) for which you get other behaviours such as:&lt;br /&gt;
The average cost remains constant as production increases.&lt;br /&gt;
&lt;br /&gt;
I&#039;ll leave up to you guys to the rest. Just pick a point or two to study. &lt;br /&gt;
Remember, there is a group evaluation at the end. Please participate so I can give each of you guys 100% in participation marks at the end.&lt;br /&gt;
&lt;br /&gt;
Alright guys, lets start this year with a blast!&lt;br /&gt;
&lt;br /&gt;
-Adam Nguyen&lt;br /&gt;
&lt;br /&gt;
I will do the next two points from where Adam left off tonight - that leaves the last 2 points&lt;br /&gt;
Christa Bicego&lt;/div&gt;</summary>
		<author><name>AdamsNguyen</name></author>
	</entry>
	<entry>
		<id>https://wiki.ubc.ca/index.php?title=Course:MATH110/Archive/2010-2011/003/Teams/Jura&amp;diff=70070</id>
		<title>Course:MATH110/Archive/2010-2011/003/Teams/Jura</title>
		<link rel="alternate" type="text/html" href="https://wiki.ubc.ca/index.php?title=Course:MATH110/Archive/2010-2011/003/Teams/Jura&amp;diff=70070"/>
		<updated>2011-01-17T08:48:14Z</updated>

		<summary type="html">&lt;p&gt;AdamsNguyen: /* Team Question 1 */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;{{Infobox MATH110 Teams&lt;br /&gt;
| team name = Jura&lt;br /&gt;
| member 1 = Adam Nguyen&lt;br /&gt;
| member 2 = Christa Bicego&lt;br /&gt;
| member 3 = Matthew Hsu&lt;br /&gt;
| member 4 = Shamilla Birring&lt;br /&gt;
}}&lt;br /&gt;
In workshop L.&lt;br /&gt;
&lt;br /&gt;
== Team Question 1 ==&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The following linear equation is a model to predict the cost of producing flags of a Canton under the assumption that the marginal cost is $7 per unit and that at the current production level of 20 items, the cost is $100.:&lt;br /&gt;
C(F) = 7F – 40&lt;br /&gt;
&lt;br /&gt;
http://www3.wolframalpha.com/Calculate/MSP/MSP27519e1i2dbedadh7bi00001ga7beg09i1456i5?MSPStoreType=image/gif&amp;amp;s=45&amp;amp;w=300&amp;amp;h=182&lt;br /&gt;
&lt;br /&gt;
This model predicts that at the production of 150 items, the cost $1010.&lt;br /&gt;
According to this model, the average cost per item will increase as production levels increase&lt;br /&gt;
Models for which the average cost remains constant as production increases:&lt;br /&gt;
C (F) = 7F&lt;br /&gt;
C (F) = F&lt;br /&gt;
&lt;br /&gt;
Hello, team Jura. This is Adam, your  new teammate. As you may be aware, there is a team question that is posted. Please take a look and be familiar with the question. We are to write a comprehensive essay on the given problem. To complete this assignment, I propose that we each pick a few points, study those points and write a paragraph on them (ex. Someone can describe the model and find out the cost of 150 units etc.) We&#039;ll then combine our information and I&#039;ll volunteer to write up a good copy.&lt;br /&gt;
&lt;br /&gt;
I have already finished the first 4 points &lt;br /&gt;
&lt;br /&gt;
Describe your model.&lt;br /&gt;
What does your model predict for a production of 150 items?&lt;br /&gt;
According yo your model, what happens to the average cost per item as production levels increase?&lt;br /&gt;
Finally, find some other models (not necessarily linear) for which you get other behaviours such as:&lt;br /&gt;
The average cost remains constant as production increases.&lt;br /&gt;
&lt;br /&gt;
I&#039;ll leave up to you guys to the rest. Just pick a point or two to study. &lt;br /&gt;
Remember, there is a group evaluation at the end. Please participate so I can give each of you guys 100% in participation marks at the end.&lt;br /&gt;
&lt;br /&gt;
Alright guys, lets start this year with a blast!&lt;br /&gt;
&lt;br /&gt;
-Adam Nguyen&lt;br /&gt;
&lt;br /&gt;
I will do the next two points from where Adam left off tonight - that leaves the last 2 points&lt;br /&gt;
Christa Bicego&lt;/div&gt;</summary>
		<author><name>AdamsNguyen</name></author>
	</entry>
	<entry>
		<id>https://wiki.ubc.ca/index.php?title=Course:MATH110/Archive/2010-2011/003/Teams/Jura&amp;diff=70069</id>
		<title>Course:MATH110/Archive/2010-2011/003/Teams/Jura</title>
		<link rel="alternate" type="text/html" href="https://wiki.ubc.ca/index.php?title=Course:MATH110/Archive/2010-2011/003/Teams/Jura&amp;diff=70069"/>
		<updated>2011-01-17T08:46:33Z</updated>

		<summary type="html">&lt;p&gt;AdamsNguyen: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;{{Infobox MATH110 Teams&lt;br /&gt;
| team name = Jura&lt;br /&gt;
| member 1 = Adam Nguyen&lt;br /&gt;
| member 2 = Christa Bicego&lt;br /&gt;
| member 3 = Matthew Hsu&lt;br /&gt;
| member 4 = Shamilla Birring&lt;br /&gt;
}}&lt;br /&gt;
In workshop L.&lt;br /&gt;
&lt;br /&gt;
== Team Question 1 ==&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The following linear equation is a model to predict the cost of producing flags of a Canton under the assumption that the marginal cost is $7 per unit and that at the current production level of 20 items, the cost is $100.:&lt;br /&gt;
C(F) = 7F – 40&lt;br /&gt;
&lt;br /&gt;
[[File:Plot.jpg]]&lt;br /&gt;
&lt;br /&gt;
This model predicts that at the production of 150 items, the cost $1010.&lt;br /&gt;
According to this model, the average cost per item will increase as production levels increase&lt;br /&gt;
Models for which the average cost remains constant as production increases:&lt;br /&gt;
C (F) = 7F&lt;br /&gt;
C (F) = F&lt;br /&gt;
&lt;br /&gt;
Hello, team Jura. This is Adam, your  new teammate. As you may be aware, there is a team question that is posted. Please take a look and be familiar with the question. We are to write a comprehensive essay on the given problem. To complete this assignment, I propose that we each pick a few points, study those points and write a paragraph on them (ex. Someone can describe the model and find out the cost of 150 units etc.) We&#039;ll then combine our information and I&#039;ll volunteer to write up a good copy.&lt;br /&gt;
&lt;br /&gt;
I have already finished the first 4 points &lt;br /&gt;
&lt;br /&gt;
Describe your model.&lt;br /&gt;
What does your model predict for a production of 150 items?&lt;br /&gt;
According yo your model, what happens to the average cost per item as production levels increase?&lt;br /&gt;
Finally, find some other models (not necessarily linear) for which you get other behaviours such as:&lt;br /&gt;
The average cost remains constant as production increases.&lt;br /&gt;
&lt;br /&gt;
I&#039;ll leave up to you guys to the rest. Just pick a point or two to study. &lt;br /&gt;
Remember, there is a group evaluation at the end. Please participate so I can give each of you guys 100% in participation marks at the end.&lt;br /&gt;
&lt;br /&gt;
Alright guys, lets start this year with a blast!&lt;br /&gt;
&lt;br /&gt;
-Adam Nguyen&lt;br /&gt;
&lt;br /&gt;
I will do the next two points from where Adam left off tonight - that leaves the last 2 points&lt;br /&gt;
Christa Bicego&lt;/div&gt;</summary>
		<author><name>AdamsNguyen</name></author>
	</entry>
	<entry>
		<id>https://wiki.ubc.ca/index.php?title=Course:MATH110/Archive/2010-2011/003/Teams/Jura&amp;diff=70068</id>
		<title>Course:MATH110/Archive/2010-2011/003/Teams/Jura</title>
		<link rel="alternate" type="text/html" href="https://wiki.ubc.ca/index.php?title=Course:MATH110/Archive/2010-2011/003/Teams/Jura&amp;diff=70068"/>
		<updated>2011-01-17T08:45:17Z</updated>

		<summary type="html">&lt;p&gt;AdamsNguyen: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;{{Infobox MATH110 Teams&lt;br /&gt;
| team name = Jura&lt;br /&gt;
| member 1 = Adam Nguyen&lt;br /&gt;
| member 2 = Christa Bicego&lt;br /&gt;
| member 3 = Matthew Hsu&lt;br /&gt;
| member 4 = Shamilla Birring&lt;br /&gt;
}}&lt;br /&gt;
In workshop L.&lt;br /&gt;
&lt;br /&gt;
== Team Question 1 ==&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The following linear equation is a model to predict the cost of producing flags of a Canton under the assumption that the marginal cost is $7 per unit and that at the current production level of 20 items, the cost is $100.:&lt;br /&gt;
C(F) = 7F – 40&lt;br /&gt;
&lt;br /&gt;
[[File:http://www3.wolframalpha.com/Calculate/MSP/MSP27519e1i2dbedadh7bi00001ga7beg09i1456i5?MSPStoreType=image/gif&amp;amp;s=45&amp;amp;w=300&amp;amp;h=182]]&lt;br /&gt;
This model predicts that at the production of 150 items, the cost $1010.&lt;br /&gt;
According to this model, the average cost per item will increase as production levels increase&lt;br /&gt;
Models for which the average cost remains constant as production increases:&lt;br /&gt;
C (F) = 7F&lt;br /&gt;
C (F) = F&lt;br /&gt;
&lt;br /&gt;
Hello, team Jura. This is Adam, your  new teammate. As you may be aware, there is a team question that is posted. Please take a look and be familiar with the question. We are to write a comprehensive essay on the given problem. To complete this assignment, I propose that we each pick a few points, study those points and write a paragraph on them (ex. Someone can describe the model and find out the cost of 150 units etc.) We&#039;ll then combine our information and I&#039;ll volunteer to write up a good copy.&lt;br /&gt;
&lt;br /&gt;
I have already finished the first 4 points &lt;br /&gt;
&lt;br /&gt;
Describe your model.&lt;br /&gt;
What does your model predict for a production of 150 items?&lt;br /&gt;
According yo your model, what happens to the average cost per item as production levels increase?&lt;br /&gt;
Finally, find some other models (not necessarily linear) for which you get other behaviours such as:&lt;br /&gt;
The average cost remains constant as production increases.&lt;br /&gt;
&lt;br /&gt;
I&#039;ll leave up to you guys to the rest. Just pick a point or two to study. &lt;br /&gt;
Remember, there is a group evaluation at the end. Please participate so I can give each of you guys 100% in participation marks at the end.&lt;br /&gt;
&lt;br /&gt;
Alright guys, lets start this year with a blast!&lt;br /&gt;
&lt;br /&gt;
-Adam Nguyen&lt;br /&gt;
&lt;br /&gt;
I will do the next two points from where Adam left off tonight - that leaves the last 2 points&lt;br /&gt;
Christa Bicego&lt;/div&gt;</summary>
		<author><name>AdamsNguyen</name></author>
	</entry>
	<entry>
		<id>https://wiki.ubc.ca/index.php?title=Thread:User_talk:ShamillaBirring/Hi&amp;diff=69977</id>
		<title>Thread:User talk:ShamillaBirring/Hi</title>
		<link rel="alternate" type="text/html" href="https://wiki.ubc.ca/index.php?title=Thread:User_talk:ShamillaBirring/Hi&amp;diff=69977"/>
		<updated>2011-01-16T02:42:12Z</updated>

		<summary type="html">&lt;p&gt;AdamsNguyen: New thread: Hi&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;Hello, team Jura. This is Adam, your  new teammate. As you may be aware, there is a team question that is posted. Please take a look and be familiar with the question. We are to write a comprehensive essay on the given problem. To complete this assignment, I propose that we each pick a few points, study those points and write a paragraph on them (ex. Someone can describe the model and find out the cost of 150 units etc.) We&#039;ll then combine our information and I&#039;ll volunteer to write up a good copy.&lt;br /&gt;
&lt;br /&gt;
I have already finished the first 4 points &lt;br /&gt;
&lt;br /&gt;
Describe your model.&lt;br /&gt;
What does your model predict for a production of 150 items?&lt;br /&gt;
According yo your model, what happens to the average cost per item as production levels increase?&lt;br /&gt;
Finally, find some other models (not necessarily linear) for which you get other behaviours such as:&lt;br /&gt;
The average cost remains constant as production increases.&lt;br /&gt;
&lt;br /&gt;
I&#039;ll leave up to you guys to the rest. Just pick a point or two to study. &lt;br /&gt;
Remember, there is a group evaluation at the end. Please participate so I can give each of you guys 100% in participation marks at the end.&lt;br /&gt;
&lt;br /&gt;
Alright guys, lets start this year with a blast!&lt;br /&gt;
&lt;br /&gt;
-Adam Nguyen&lt;/div&gt;</summary>
		<author><name>AdamsNguyen</name></author>
	</entry>
	<entry>
		<id>https://wiki.ubc.ca/index.php?title=User_talk:Matthew&amp;diff=69976</id>
		<title>User talk:Matthew</title>
		<link rel="alternate" type="text/html" href="https://wiki.ubc.ca/index.php?title=User_talk:Matthew&amp;diff=69976"/>
		<updated>2011-01-16T02:40:34Z</updated>

		<summary type="html">&lt;p&gt;AdamsNguyen: /* Remarks on your essay */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;==Hi!==&lt;br /&gt;
&lt;br /&gt;
Hello, team Jura. This is Adam, your  new teammate. As you may be aware, there is a team question that is posted. Please take a look and be familiar with the question. We are to write a comprehensive essay on the given problem. To complete this assignment, I propose that we each pick a few points, study those points and write a paragraph on them (ex. Someone can describe the model and find out the cost of 150 units etc.) We&#039;ll then combine our information and I&#039;ll volunteer to write up a good copy.&lt;br /&gt;
&lt;br /&gt;
I have already finished the first 4 points &lt;br /&gt;
&lt;br /&gt;
Describe your model.&lt;br /&gt;
What does your model predict for a production of 150 items?&lt;br /&gt;
According yo your model, what happens to the average cost per item as production levels increase?&lt;br /&gt;
Finally, find some other models (not necessarily linear) for which you get other behaviours such as:&lt;br /&gt;
The average cost remains constant as production increases.&lt;br /&gt;
&lt;br /&gt;
I&#039;ll leave up to you guys to the rest. Just pick a point or two to study. &lt;br /&gt;
Remember, there is a group evaluation at the end. Please participate so I can give each of you guys 100% in participation marks at the end.&lt;br /&gt;
&lt;br /&gt;
Alright guys, lets start this year with a blast!&lt;br /&gt;
&lt;br /&gt;
-Adam Nguyen &lt;br /&gt;
&lt;br /&gt;
==Remarks on your essay==&lt;br /&gt;
&lt;br /&gt;
Hi Matthew,&amp;lt;br/&amp;gt;&lt;br /&gt;
Thanks for contributing to the wiki with your essay, I liked the theme you picked. Here&#039;s some feedback for you.&lt;br /&gt;
&lt;br /&gt;
* When citing your sources, consider using the &amp;lt;nowiki&amp;gt;&amp;lt;ref&amp;gt;&amp;lt;/ref&amp;gt;&amp;lt;/nowiki&amp;gt; tag which produces something like this&amp;lt;ref&amp;gt;http://wiki.ubc.ca/Help:Formatting#Footnotes&amp;lt;/ref&amp;gt;. If you do so, you then need to add the tag&amp;lt;nowiki&amp;gt;&amp;lt;references/&amp;gt;&amp;lt;/nowiki&amp;gt;where you would like to see your references collected. See the code for this page to see how I did this or check the reference.&lt;br /&gt;
&lt;br /&gt;
Best&amp;lt;br/&amp;gt;&lt;br /&gt;
-- [[User:DavidKohler|DavidKohler]]&lt;br /&gt;
&lt;br /&gt;
=====Sources=====&lt;br /&gt;
&amp;lt;references/&amp;gt;&lt;/div&gt;</summary>
		<author><name>AdamsNguyen</name></author>
	</entry>
	<entry>
		<id>https://wiki.ubc.ca/index.php?title=User_talk:ChristaBicego&amp;diff=69975</id>
		<title>User talk:ChristaBicego</title>
		<link rel="alternate" type="text/html" href="https://wiki.ubc.ca/index.php?title=User_talk:ChristaBicego&amp;diff=69975"/>
		<updated>2011-01-16T02:39:20Z</updated>

		<summary type="html">&lt;p&gt;AdamsNguyen: Talk page autocreated when first thread was posted.&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;&lt;/div&gt;</summary>
		<author><name>AdamsNguyen</name></author>
	</entry>
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