UBC Wiki - User contributions [en]

Course:MATH110/Archive/2010-2011/003/Teams/Jura/Homework/13 Part3

2011-02-03T22:01:28Z

ChristaBicego:

== Jura Corporation: We used to make fine Swiss cheese... until the earthquake. ==

Our recent expansion into the fine art of cheese making was doing extremely well. It wasn't surprising! We had thousands of orders and even the rats in the city were congregating in our warehouse! Luckily, our mathematical prowess convinced our CEO, the one who shall not be named, to invoke extreme prejudice on those nasty critters. With the business saved, all was good... until the earthquake. Yes... the earthquake! Our warehouse could not handle the force of the earthquake and the unfortunate event brought our cheese business to an halt. Although our CEO is quite angry, he has re-mortgaged his house to pay for our new warehouse, but he wants to ensure that our next warehouse can actually withstand a future earthquake. Enough of this, it's time to suit up and do some math!


== An Introduction to the Richter Magnitude Scale ==

Seismic waves are defined as the vibrations from earthquakes that travel through the Earth <ref>http://inventors.about.com/od/qrstartinventors/a/Charles_Richter.htm</ref>. With the definition of what seismic waves are, it was interesting to discuss the possibility of a method to accurately compare different earthquakes with each other. Charles Richter, a Physicist, found this to be a topic of fascination. It was such a great topic of interest for him that in 1935, Richter was able to accurately measure the magnitude of an earthquake <ref>http://inventors.about.com/od/qrstartinventors/a/Charles_Richter.htm</ref>.



Richter described his scale in the following way: 1) The magnitude of an earthquake is determined from the logarithm of the amplitude of waves recorded by seismographs <ref>http://earthquake.usgs.gov/learn/topics/richter.php</ref>. 2) The magnitude is represented by real numbers. For example, the real number, 6.5, would describe the magnitude of a particular earthquake. With what we know about Logarithms, we know that whenever there is an increase in the whole number (e.g., 4.5 to 5.5) there will be a tenfold increase in magnitude. A more mathematical explanation will be detailed in the next section.



Listed below is a graph outlining the effects of different magnitudes of earthquakes <ref>-https://secureweb.wooster.edu/seismic/Images/RICHTER.gif-</ref>.
<center>http://i.imgur.com/YM33y.gif</center>


== The Richter Magnitude Scale: An Application on How it Works on a Logarithmic Scale ==

Description goes here.


== Gentlemen, we can rebuild it. We have the technology. We have the capability to build an earthquake resistant building. Jura Corporation will be that building. Better than it was before. Better, stronger, classier. ==

Description goes here.
 
Log base 10 and the Richter Scale 
Lets start by defining: 
Base-10: simple- is a logarithmic with 10 as its base and is commonly seen in roman numerals or you guessed it, Richter Magnitude Scale 
logarithmic scale: A scaled measurement. Logarithmic scales use logs to represent a quantity instead of using the actual quantity. 
An example from wiki: 
1,10,100,1000 instead of 1,2,3,4 
This is also an example of how logarithmic scales are used with the Richter Magnitude scale. 

For the Richter's scale log base-10 denotes the amount of seismic energy released by an earthquake. The number equated for the earthquake represents its strength and increases as the number becomes larger. A 6.0 magnitude earthquake is 10 times larger than a 5.0 magnitude earthquake. This is so because each whole number increases are broken up into ten .1 increments; from 5.1- 6.0. So, now to how the the Richter Magnitude Scale uses a base-10 logarithmic scale. The final quantity (the magnitude) is found by deriving the logarithm of the wave amplitude recorded on a seismograph. The equation is: 
M2= log10A - log10A0(S) 
A= maximum excursion of the needle on the "Wood-Anderson" seismograph 
A0= the distance from the epicenter to the station(S) 

== References ==
<references/>

Course:MATH110/Archive/2010-2011/003/Teams/Jura/Homework/13 Part3

2011-02-03T21:57:08Z

ChristaBicego:

== Jura Corporation: We used to make fine Swiss cheese... until the earthquake. ==

Our recent expansion into the fine art of cheese making was doing extremely well. It wasn't surprising! We had thousands of orders and even the rats in the city were congregating in our warehouse! Luckily, our mathematical prowess convinced our CEO, the one who shall not be named, to invoke extreme prejudice on those nasty critters. With the business saved, all was good... until the earthquake. Yes... the earthquake! Our warehouse could not handle the force of the earthquake and the unfortunate event brought our cheese business to an halt. Although our CEO is quite angry, he has re-mortgaged his house to pay for our new warehouse, but he wants to ensure that our next warehouse can actually withstand a future earthquake. Enough of this, it's time to suit up and do some math!


== An Introduction to the Richter Magnitude Scale ==

Seismic waves are defined as the vibrations from earthquakes that travel through the Earth <ref>http://inventors.about.com/od/qrstartinventors/a/Charles_Richter.htm</ref>. With the definition of what seismic waves are, it was interesting to discuss the possibility of a method to accurately compare different earthquakes with each other. Charles Richter, a Physicist, found this to be a topic of fascination. It was such a great topic of interest for him that in 1935, Richter was able to accurately measure the magnitude of an earthquake <ref>http://inventors.about.com/od/qrstartinventors/a/Charles_Richter.htm</ref>.



Richter described his scale in the following way: 1) The magnitude of an earthquake is determined from the logarithm of the amplitude of waves recorded by seismographs <ref>http://earthquake.usgs.gov/learn/topics/richter.php</ref>. 2) The magnitude is represented by real numbers. For example, the real number, 6.5, would describe the magnitude of a particular earthquake. With what we know about Logarithms, we know that whenever there is an increase in the whole number (e.g., 4.5 to 5.5) there will be a tenfold increase in magnitude. A more mathematical explanation will be detailed in the next section.



Listed below is a graph outlining the effects of different magnitudes of earthquakes <ref>-https://secureweb.wooster.edu/seismic/Images/RICHTER.gif-</ref>.
<center>http://i.imgur.com/YM33y.gif</center>


== The Richter Magnitude Scale: An Application on How it Works on a Logarithmic Scale ==

Description goes here.


== Gentlemen, we can rebuild it. We have the technology. We have the capability to build an earthquake resistant building. Jura Corporation will be that building. Better than it was before. Better, stronger, classier. ==

Description goes here.
 
Log base 10 and the Richter Scale 
Lets start by defining: 
Base-10: simple- is a logarithmic with 10 as its base and is commonly seen in roman numerals or you guessed it, Richter Magnitude Scale 
logarithmic scale: A scaled measurement. Logarithmic scales use logs to represent a quantity instead of using the actual quantity. 
An example from wiki: 
1,10,100,1000 instead of 1,2,3,4 
This is also an example of how logarithmic scales are used with the Richter Magnitude scale. 
For the Richter's scale log base-10 denotes the amount of seismic energy released by an earthquake. The number equated for the earthquake represents its strength and increases as the number becomes larger. A 6.0 magnitude earthquake is 10 times larger than a 5.0 magnitude earthquake. This is so because each whole number increases are broken up into ten .1 increments; from 5.1- 6.0. So, now to how the the Richter Magnitude Scale uses a base-10 logarithmic scale. The final quantity (the magnitude) is found by deriving the logarithm of the wave amplitude recorded on a seismograph. The equation is: 
M2= log10A - log10A0(S)

== References ==
<references/>

Course:MATH110/Archive/2010-2011/003/Teams/Jura/Homework/13 Part3

2011-02-03T21:50:34Z

ChristaBicego:

== Jura Corporation: We used to make fine Swiss cheese... until the earthquake. ==

Our recent expansion into the fine art of cheese making was doing extremely well. It wasn't surprising! We had thousands of orders and even the rats in the city were congregating in our warehouse! Luckily, our mathematical prowess convinced our CEO, the one who shall not be named, to invoke extreme prejudice on those nasty critters. With the business saved, all was good... until the earthquake. Yes... the earthquake! Our warehouse could not handle the force of the earthquake and the unfortunate event brought our cheese business to an halt. Although our CEO is quite angry, he has re-mortgaged his house to pay for our new warehouse, but he wants to ensure that our next warehouse can actually withstand a future earthquake. Enough of this, it's time to suit up and do some math!


== An Introduction to the Richter Magnitude Scale ==

Seismic waves are defined as the vibrations from earthquakes that travel through the Earth <ref>http://inventors.about.com/od/qrstartinventors/a/Charles_Richter.htm</ref>. With the definition of what seismic waves are, it was interesting to discuss the possibility of a method to accurately compare different earthquakes with each other. Charles Richter, a Physicist, found this to be a topic of fascination. It was such a great topic of interest for him that in 1935, Richter was able to accurately measure the magnitude of an earthquake <ref>http://inventors.about.com/od/qrstartinventors/a/Charles_Richter.htm</ref>.



Richter described his scale in the following way: 1) The magnitude of an earthquake is determined from the logarithm of the amplitude of waves recorded by seismographs <ref>http://earthquake.usgs.gov/learn/topics/richter.php</ref>. 2) The magnitude is represented by real numbers. For example, the real number, 6.5, would describe the magnitude of a particular earthquake. With what we know about Logarithms, we know that whenever there is an increase in the whole number (e.g., 4.5 to 5.5) there will be a tenfold increase in magnitude. A more mathematical explanation will be detailed in the next section.



Listed below is a graph outlining the effects of different magnitudes of earthquakes <ref>-https://secureweb.wooster.edu/seismic/Images/RICHTER.gif-</ref>.
<center>http://i.imgur.com/YM33y.gif</center>


== The Richter Magnitude Scale: An Application on How it Works on a Logarithmic Scale ==

Description goes here.


== Gentlemen, we can rebuild it. We have the technology. We have the capability to build an earthquake resistant building. Jura Corporation will be that building. Better than it was before. Better, stronger, classier. ==

Description goes here.

Log base 10 and the Richter Scale 
Lets start by defining: 
Base-10: simple- is a logarithmic with 10 as its base and is commonly seen in roman numerals or you guessed it, Richter Magnitude Scale 
logarithmic scale: A scaled measurement. Logarithmic scales use logs to represent a quantity instead of using the actual quantity. 
An example from wiki: 
1,10,100,1000 instead of 1,2,3,4 
This is also an example of how logarithmic scales are used with the Richter Magnitude scale. 
For the Richter's scale log base-10 denotes the amount of seismic energy released by an earthquake. 

== References ==
<references/>

Course:MATH110/Archive/2010-2011/003/Teams/Jura

2011-01-28T15:49:10Z

ChristaBicego:

{{Infobox MATH110 Teams
| team name = Jura
| member 1 = [mailto:adam@premierwestmma.com Adam Nguyen] - Grapple
| member 2 = Christa Bicego - Achieve
| member 3 = [mailto:matthew.hsu@gmail.com Matthew Hsu] - Happy
| member 4 = Shamilla Birring - Smile
}}

== Workshop ==
In workshop L. 

Pick one of the topic offered below and then explain in your own words what it means that these concepts work on a logarithmic scale. Create a wiki page with all your explanations. The length of that page is up to you, but it should feel like the work of four people thinking about a topic and trying to make sense of it. If you drafted something and would like some comments (within 24 hours), send me an email and a link where to look at, I'll post comments). 

Topics: 
Decibels (Christa Bicego) 
Richter magnitude scale 
Brightness of stars 
pH 
Put your name beside the one you are going to do.

== Homework ==
http://wiki.ubc.ca/Course:MATH110/003/Teams/Jura/Homework/

User:ChristaBicego

2011-01-27T22:29:41Z

ChristaBicego:

Christa Bicego

I'm majoring in biology and hopefully attending veterinary school in September of 2012. Mathematics is found everywhere in biology and science as a whole. An example of math in my everyday studies is, mathematics aiding in predicting population trends. Past data could be used to plot and graph for a visual representation of past populations. With the x-axis possibly being time and the y-axis being population. Seeing the data in a graph allows for one to see the increases, decreases, and carrying capacity (horizontal asymptote) of the population. Algebra, a common concept of mathematics is used to produce a formula/ equation to predict the population in a given year (or time). Another example is during lab experiments, I spend a lot of time examining (testing) an organism and recording data. A lot of the time the data consists of numbers. These numbers are very important when deciding if the experiment is significantly significant and if it can support the hypothesis. When the data is substituted into say ... either a chi-squared or 95% confidence interval formula one can determine if their hypothesis stands or is rejected. These are two simple examples of how mathematics is used in science and specifically biology. I believe the whole concept of science is built upon math.

User:ChristaBicego

2011-01-27T22:17:17Z

ChristaBicego:

Christa Bicego

I'm majoring in biology and hopefully attending veterinary school in September of 2012. Math is found everywhere in biology and science as a whole. An example of math in my everyday studies is, mathematics aiding in predicting population trends. Past data could be used to plot and graph for a visual representation of past populations. With the x-axis possible being time and the y-axis being population. Seeing the data in a graph allows for one to see the increases, decreases, and carrying capacity of the population (horizontal asymptote). Algebra, a common concept of mathematics is used to produce a formula/ equation to predict that population in a given year (or time).

User:ChristaBicego

2011-01-27T22:15:00Z

ChristaBicego:

User:ChristaBicego

2011-01-27T17:17:44Z

ChristaBicego:

Christa Bicego

I'm majoring in biology and hopefully one day going to veterinary school. Math is found everywhere in biology and in science as a whole.

Course:MATH110/Archive/2010-2011/003/Teams/Jura/Homework/11 Part3

2011-01-19T01:16:01Z

ChristaBicego:

Write a linear model to predict the cost of producing flags of your team'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.



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.




Describe your model.



[[File:plot123.gif]]



What does your model predict for a production of 150 items?



This model predicts that at the production of 150 items, the cost $1010.



According to your model, what happens to the average cost per item as production levels increase?



According to this model, the average cost per item will increase as production levels increase.



The average cost remains constant as production increases.



C (F) = 7F
C (F) = F



The average cost diminishes as production increases (-,+)




Average Cost= total cost/ production 
 
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. 
C(10)= 400(10)+ x 
C(10) = 4000 + x 
5000- 4000 = x 
x= 1000 
 
C(F)= 400F + 1000 

Average Cost= total cost/ production 
C(10)= 400(10) +1000 = 5000/10 = 500 
C(20) = 400(20) +1000 = 9000/20 = 450 
C(25)= 400(25) +1000 = 11000/ 25 = 440 

Conclusion: the data shows that the average cost becomes smaller as production increases 
AvgC becomes smaller when Production increases 




The average cost increases as production increases.



Average cost becomes larger when Production becomes larger ( +,+) 

Average Cost= total cost/ production 

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 

C(F)= 8F - 200 

The average cost is getting larger when production becomes larger shown by substituting larger production quantities into the function for F. 

C(50)= 8(50)- 200 = 200 

C(51)= 8(51)- 200 = 208 

Average Cost= total cost/ production 

C(50)= 200/ 50 = 4 
C(51)= 208/51 = 4.07 

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. 




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.



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's production level increases.



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.



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'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.



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.



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.



I'll need to manually graph this out and scan it in.



Other interesting properties that you can think of and create a model for.



Solution goes here.


== Discussion ==

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'll then combine our information and I'll volunteer to write up a good copy.



I have already finished the first 4 points



Describe your model.
What does your model predict for a production of 150 items?
According yo your model, what happens to the average cost per item as production levels increase?
Finally, find some other models (not necessarily linear) for which you get other behaviours such as:
The average cost remains constant as production increases.



I'll leave up to you guys to the rest. Just pick a point or two to study.
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.



Alright guys, lets start this year with a blast!



-Adam Nguyen



I will do the next two points from where Adam left off tonight - that leaves the last 2 points.



-Christa Bicego



Since there are two points left, I'll work on the Economies of Scale model.
 
-Matthew



Alright, I have the framework for our economy of scale question. I think it's correct, but any feedback on it would be appreciated. If everything looks alright, I'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.
 
-Matthew



Just did some formatting on our page to give it some structure. If you're unfamiliar with posting on the Wiki, I've templated where you can copy and paste your responses into to make things a bit easier.
 
-Matthew

Course:MATH110/Archive/2010-2011/003/Teams/Jura/Homework/11 Part3

2011-01-19T01:14:42Z

ChristaBicego:

Write a linear model to predict the cost of producing flags of your team'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.



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.




Describe your model.



[[File:plot123.gif]]



What does your model predict for a production of 150 items?



This model predicts that at the production of 150 items, the cost $1010.



According to your model, what happens to the average cost per item as production levels increase?



According to this model, the average cost per item will increase as production levels increase.



The average cost remains constant as production increases.



C (F) = 7F
C (F) = F



The average cost diminishes as production increases (-,+)




Average Cost= total cost/ production 
 
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. 
C(10)= 400(10)+ x 
C(10) = 4000 + x 
5000- 4000 = x 
x= 1000 
 
C(F)= 400F + 1000 

Average Cost= total cost/ production 
C(10)= 400(10) +1000 = 5000/10 = 500 
C(20) = 400(20) +1000 = 9000/20 = 450 
C(25)= 400(25) +1000 = 11000/ 25 = 440 

Conclusion: the data shows that the average cost becomes smaller as production increases 
AvgC becomes smaller when Production increases 

A 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 

C(F)= 8F - 200 

The average cost is getting larger when production becomes larger shown by substituting larger production quantities into the function for F. 

C(50)= 8(50)- 200 = 200 

C(51)= 8(51)- 200 = 208 

Average Cost= total cost/ production 

C(50)= 200/ 50 = 4 
C(51)= 208/51 = 4.07 

Average cost




The average cost increases as production increases.



Average cost becomes larger when Production becomes larger ( +,+) 

Average Cost= total cost/ production 

A 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 

C(F)= 8F - 200 

The average cost is getting larger when production becomes larger shown by substituting larger production quantities into the function for F. 

C(50)= 8(50)- 200 = 200 

C(51)= 8(51)- 200 = 208 

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. 




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.



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's production level increases.



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.



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'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.



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.



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.



I'll need to manually graph this out and scan it in.



Other interesting properties that you can think of and create a model for.



Solution goes here.


== Discussion ==

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'll then combine our information and I'll volunteer to write up a good copy.



I have already finished the first 4 points



Describe your model.
What does your model predict for a production of 150 items?
According yo your model, what happens to the average cost per item as production levels increase?
Finally, find some other models (not necessarily linear) for which you get other behaviours such as:
The average cost remains constant as production increases.



I'll leave up to you guys to the rest. Just pick a point or two to study.
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.



Alright guys, lets start this year with a blast!



-Adam Nguyen



I will do the next two points from where Adam left off tonight - that leaves the last 2 points.



-Christa Bicego



Since there are two points left, I'll work on the Economies of Scale model.
 
-Matthew



Alright, I have the framework for our economy of scale question. I think it's correct, but any feedback on it would be appreciated. If everything looks alright, I'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.
 
-Matthew



Just did some formatting on our page to give it some structure. If you're unfamiliar with posting on the Wiki, I've templated where you can copy and paste your responses into to make things a bit easier.
 
-Matthew

Course:MATH110/Archive/2010-2011/003/Teams/Jura/Homework/11 Part3

2011-01-19T01:06:59Z

ChristaBicego:

Write a linear model to predict the cost of producing flags of your team'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.



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.




Describe your model.



[[File:plot123.gif]]



What does your model predict for a production of 150 items?



This model predicts that at the production of 150 items, the cost $1010.



According to your model, what happens to the average cost per item as production levels increase?



According to this model, the average cost per item will increase as production levels increase.



The average cost remains constant as production increases.



C (F) = 7F
C (F) = F



The average cost diminishes as production increases (-,+)



AvgC becomes smaller when Production increases 

A 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 

C(F)= 8F - 200 

The average cost is getting larger when production becomes larger shown by substituting larger production quantities into the function for F. 

C(50)= 8(50)- 200 = 200 

C(51)= 8(51)- 200 = 208 

Average Cost= total cost/ production 

C(50)= 200/ 50 = 4 
C(51)= 208/51 = 4.07 

Average cost




The average cost increases as production increases.



Average cost becomes larger when Production becomes larger ( +,+) 

Average Cost= total cost/ production 

A 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 

C(F)= 8F - 200 

The average cost is getting larger when production becomes larger shown by substituting larger production quantities into the function for F. 

C(50)= 8(50)- 200 = 200 

C(51)= 8(51)- 200 = 208 

Average Cost= total cost/ production 
 
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. 
C(10)= 400(10)+ x 
C(10) = 4000 + x 
5000- 4000 = x 
x= 1000 
 
C(F)= 400F + 1000 

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. 




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.



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's production level increases.



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.



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'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.



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.



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.



I'll need to manually graph this out and scan it in.



Other interesting properties that you can think of and create a model for.



Solution goes here.


== Discussion ==

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'll then combine our information and I'll volunteer to write up a good copy.



I have already finished the first 4 points



Describe your model.
What does your model predict for a production of 150 items?
According yo your model, what happens to the average cost per item as production levels increase?
Finally, find some other models (not necessarily linear) for which you get other behaviours such as:
The average cost remains constant as production increases.



I'll leave up to you guys to the rest. Just pick a point or two to study.
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.



Alright guys, lets start this year with a blast!



-Adam Nguyen



I will do the next two points from where Adam left off tonight - that leaves the last 2 points.



-Christa Bicego



Since there are two points left, I'll work on the Economies of Scale model.
 
-Matthew



Alright, I have the framework for our economy of scale question. I think it's correct, but any feedback on it would be appreciated. If everything looks alright, I'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.
 
-Matthew



Just did some formatting on our page to give it some structure. If you're unfamiliar with posting on the Wiki, I've templated where you can copy and paste your responses into to make things a bit easier.
 
-Matthew

Course:MATH110/Archive/2010-2011/003/Teams/Jura/Homework/11 Part3

2011-01-19T00:56:38Z

ChristaBicego:

Write a linear model to predict the cost of producing flags of your team'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.



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.




Describe your model.



[[File:plot123.gif]]



What does your model predict for a production of 150 items?



This model predicts that at the production of 150 items, the cost $1010.



According to your model, what happens to the average cost per item as production levels increase?



According to this model, the average cost per item will increase as production levels increase.



The average cost remains constant as production increases.



C (F) = 7F
C (F) = F



The average cost diminishes as production increases (-,+)



AvgC becomes smaller when Production increases 

Average Cost= total cost/ production 
 
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. 
C(10)= 400(10)+ x 
C(10) = 4000 + x 
5000- 4000 = x 
x= 1000 
 
C(F)= 400F + 1000




The average cost increases as production increases.



Average cost becomes larger when Production becomes larger ( +,+) 

Average Cost= total cost/ production 

A 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 

C(F)= 8F - 200 

The average cost is getting larger when production becomes larger shown by substituting larger production quantities into the function for F. 

C(50)= 8(50)- 200 = 200 

C(51)= 8(51)- 200 = 208 

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. 




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.



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's production level increases.



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.



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'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.



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.



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.



I'll need to manually graph this out and scan it in.



Other interesting properties that you can think of and create a model for.



Solution goes here.


== Discussion ==

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'll then combine our information and I'll volunteer to write up a good copy.



I have already finished the first 4 points



Describe your model.
What does your model predict for a production of 150 items?
According yo your model, what happens to the average cost per item as production levels increase?
Finally, find some other models (not necessarily linear) for which you get other behaviours such as:
The average cost remains constant as production increases.



I'll leave up to you guys to the rest. Just pick a point or two to study.
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.



Alright guys, lets start this year with a blast!



-Adam Nguyen



I will do the next two points from where Adam left off tonight - that leaves the last 2 points.



-Christa Bicego



Since there are two points left, I'll work on the Economies of Scale model.
 
-Matthew



Alright, I have the framework for our economy of scale question. I think it's correct, but any feedback on it would be appreciated. If everything looks alright, I'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.
 
-Matthew



Just did some formatting on our page to give it some structure. If you're unfamiliar with posting on the Wiki, I've templated where you can copy and paste your responses into to make things a bit easier.
 
-Matthew

Course:MATH110/Archive/2010-2011/003/Teams/Jura/Homework/11 Part3

2011-01-19T00:47:17Z

ChristaBicego:

Write a linear model to predict the cost of producing flags of your team'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.



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.




Describe your model.



[[File:plot123.gif]]



What does your model predict for a production of 150 items?



This model predicts that at the production of 150 items, the cost $1010.



According to your model, what happens to the average cost per item as production levels increase?



According to this model, the average cost per item will increase as production levels increase.



The average cost remains constant as production increases.



C (F) = 7F
C (F) = F



The average cost diminishes as production increases (-,+)



AvgC becomes smaller when Production increases

Average Cost= total cost/ production

AvgC= C - P



The average cost increases as production increases.



Average cost becomes larger when Production becomes larger ( +,+) 

Average Cost= total cost/ production 

A 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 

C(F)= 8F - 200 

The average cost is getting larger when production becomes larger shown by substituting larger production quantities into the function for F. 

C(50)= 8(50)- 200 = 200 

C(51)= 8(51)- 200 = 208 

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. 




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.



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's production level increases.



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.



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'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.



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.



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.



I'll need to manually graph this out and scan it in.



Other interesting properties that you can think of and create a model for.



Solution goes here.


== Discussion ==

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'll then combine our information and I'll volunteer to write up a good copy.



I have already finished the first 4 points



Describe your model.
What does your model predict for a production of 150 items?
According yo your model, what happens to the average cost per item as production levels increase?
Finally, find some other models (not necessarily linear) for which you get other behaviours such as:
The average cost remains constant as production increases.



I'll leave up to you guys to the rest. Just pick a point or two to study.
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.



Alright guys, lets start this year with a blast!



-Adam Nguyen



I will do the next two points from where Adam left off tonight - that leaves the last 2 points.



-Christa Bicego



Since there are two points left, I'll work on the Economies of Scale model.
 
-Matthew



Alright, I have the framework for our economy of scale question. I think it's correct, but any feedback on it would be appreciated. If everything looks alright, I'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.
 
-Matthew



Just did some formatting on our page to give it some structure. If you're unfamiliar with posting on the Wiki, I've templated where you can copy and paste your responses into to make things a bit easier.
 
-Matthew

Course:MATH110/Archive/2010-2011/003/Teams/Jura/Homework/11 Part3

2011-01-19T00:44:28Z

ChristaBicego:

Write a linear model to predict the cost of producing flags of your team'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.



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.




Describe your model.



[[File:plot123.gif]]



What does your model predict for a production of 150 items?



This model predicts that at the production of 150 items, the cost $1010.



According to your model, what happens to the average cost per item as production levels increase?



According to this model, the average cost per item will increase as production levels increase.



The average cost remains constant as production increases.



C (F) = 7F
C (F) = F



The average cost diminishes as production increases (-,+)



AvgC becomes smaller when Production increases

Average Cost= total cost/ production

AvgC= C - P



The average cost increases as production increases.



Average cost becomes larger when Production becomes larger ( +,+)

Average Cost= total cost/ production

A 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

C(F)= 8F - 200

The average cost is getting larger when production becomes larger shown by substituting larger production quantities into the function for F.

C(50)= 8(50)- 200 = 200

C(51)= 8(51)- 200 = 208

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.




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.



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's production level increases.



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.



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'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.



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.



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.



I'll need to manually graph this out and scan it in.



Other interesting properties that you can think of and create a model for.



Solution goes here.


== Discussion ==

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'll then combine our information and I'll volunteer to write up a good copy.



I have already finished the first 4 points



Describe your model.
What does your model predict for a production of 150 items?
According yo your model, what happens to the average cost per item as production levels increase?
Finally, find some other models (not necessarily linear) for which you get other behaviours such as:
The average cost remains constant as production increases.



I'll leave up to you guys to the rest. Just pick a point or two to study.
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.



Alright guys, lets start this year with a blast!



-Adam Nguyen



I will do the next two points from where Adam left off tonight - that leaves the last 2 points.



-Christa Bicego



Since there are two points left, I'll work on the Economies of Scale model.
 
-Matthew



Alright, I have the framework for our economy of scale question. I think it's correct, but any feedback on it would be appreciated. If everything looks alright, I'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.
 
-Matthew



Just did some formatting on our page to give it some structure. If you're unfamiliar with posting on the Wiki, I've templated where you can copy and paste your responses into to make things a bit easier.
 
-Matthew

Course:MATH110/Archive/2010-2011/003/Teams/Jura/Homework/11 Part3

2011-01-19T00:36:21Z

ChristaBicego:

Write a linear model to predict the cost of producing flags of your team'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.



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.




Describe your model.



[[File:plot123.gif]]



What does your model predict for a production of 150 items?



This model predicts that at the production of 150 items, the cost $1010.



According to your model, what happens to the average cost per item as production levels increase?



According to this model, the average cost per item will increase as production levels increase.



The average cost remains constant as production increases.



C (F) = 7F
C (F) = F



The average cost diminishes as production increases (-,+)



AvgC becomes smaller when Production increases

Average Cost= total cost/ production

AvgC= C - P



The average cost increases as production increases.



Average cost becomes larger when Production becomes larger ( +,+)

Average Cost= total cost/ production

Average Cost= C + P

A new model: The marginal cost of a pair of runners is $20 dollars per unit and that at the current production level of 50 items, the cost is $200 dollars

C(F)= 20F -




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.



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's production level increases.



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.



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'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.



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.



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.



I'll need to manually graph this out and scan it in.



Other interesting properties that you can think of and create a model for.



Solution goes here.


== Discussion ==

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'll then combine our information and I'll volunteer to write up a good copy.



I have already finished the first 4 points



Describe your model.
What does your model predict for a production of 150 items?
According yo your model, what happens to the average cost per item as production levels increase?
Finally, find some other models (not necessarily linear) for which you get other behaviours such as:
The average cost remains constant as production increases.



I'll leave up to you guys to the rest. Just pick a point or two to study.
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.



Alright guys, lets start this year with a blast!



-Adam Nguyen



I will do the next two points from where Adam left off tonight - that leaves the last 2 points.



-Christa Bicego



Since there are two points left, I'll work on the Economies of Scale model.
 
-Matthew



Alright, I have the framework for our economy of scale question. I think it's correct, but any feedback on it would be appreciated. If everything looks alright, I'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.
 
-Matthew



Just did some formatting on our page to give it some structure. If you're unfamiliar with posting on the Wiki, I've templated where you can copy and paste your responses into to make things a bit easier.
 
-Matthew

Course:MATH110/Archive/2010-2011/003/Teams/Jura

2011-01-16T19:15:17Z

ChristaBicego:

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'll then combine our information and I'll volunteer to write up a good copy.

I have already finished the first 4 points

Describe your model.
What does your model predict for a production of 150 items?
According yo your model, what happens to the average cost per item as production levels increase?
Finally, find some other models (not necessarily linear) for which you get other behaviours such as:
The average cost remains constant as production increases.

I'll leave up to you guys to the rest. Just pick a point or two to study.
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.

Alright guys, lets start this year with a blast!

-Adam Nguyen

Infobox MATH110 Teams
| team name = Jura
| member 1 = Adam Nguyen
| member 2 = Christa Bicego
| member 3 = Matthew Hsu
| member 4 = Shamilla Birring
}}
In workshop L.

I will do the next two points from where Adam left off tonight - that leaves the last 2 points
Christa Bicego

Course talk:MATH110/003/Teams/Jura

2011-01-16T19:14:34Z

ChristaBicego: Talk page autocreated when first thread was posted.

Thread:Course talk:MATH110/003/Teams/Jura/math homework

2011-01-16T19:14:34Z

ChristaBicego: New thread: math homework

I will do the next 2 point after Adams points

Course:MATH110/Archive/2010-2011/003/Groups/Group 17/Basic Skills Project

2010-12-02T17:12:35Z

ChristaBicego:

==The Pythagorean Theorem==

=== What Is It? ===
'''History:'''

Developed by a man named Pythagoras was born in the late 6th century B.C. on the island of Samos Greece. He proved that for any right hand triangle, the two shorter sides squared and added together exactly equal the squared amount of the longest side. This looks like:
a^2 + b^2 = c^2

'''Pythagorean Basics:'''

1) Only works for triangles

2) Only works for triangles with a right hand angle (90 degrees)

[[File:500px-Pythagorean.svg.png]]

This diagram demonstrates the use of pythagorean theorem to calculate the area of the square on the hypothenus- c. This is possible by summing the squared areas of the smaller sides - a and b

Area of a triangle -> (1/2)(base)(height)

Christa Bicego

=== How Do We Know It's True? ===
[[User:BenJeffery|BenJeffery]]

There are many proofs of the theorem. One of the most straightforward is the following:

Take four right-angled triangles and connect them into a square as shown, so that they hypotenuses form an inner square as follows:

[[File:Proof_2.png]]

We can see that the length of each side of the outer square is <math>a+b</math>, and that the area must be <math>(a+b)^2</math>.

The pieces of the square are the inner square and our four triangles.

The area of each triangle can be given as <math>(1/2)ab</math>.

Meanwhile, the inner square has side length of <math>c</math>, and area of <math>c^2</math>.

From this, we can see that:

<math>(a+b)^2 = 2ab + c^2</math>

Expanding, we see that:

<math>a^2+2ab+b^2 = 2ab +c^2</math>

Balance the equation by subtracting <math>2ab</math> to get:

<math>a^2+b^2 = c^2</math>

This is, of course, the formula for the theorem!

If you prefer a more straight-forward visual proof, watch the following video. It clearly shows that the water in the two smaller squares (formed by squaring the length of the smaller sides) fits perfectly into the square formed from the hypotenuse.

{{#ev:youtube | CAkMUdeB06o | 400}}

=== How Do You Use It? ===

Explain how to apply the theorem to simple, as well as more complex examples. Verbal as well as mathematical examples are good.

Real-life application

There are many different real-life situations which involve the Pythagorean theorem.

For example, let’s assume two friends Fred and Matt want to meet at a specific point (ex: shopping mall). Fred is 8 Km away from the mall and Matt is 7 km away (assume they are at a right angle from each other in comparison to the mall), how do we find the distance between the two of them? By using the Pythagorean theorem we are able to determine the distance between them.

<math>5^2 + 7^2=74 </math>

<math>\sqrt {74} = 8.6 km </math>

8.6 is the distance that Fred and Matt are from each other

Another example of a real-life application of the Pythagorean theorem would be on how to figure out the necessary height of an object. Lets suppose you have a 15 meter high wall. You want to find out how long a ladder has to be if it is 5 meters from the base of the wall. Implementing the Pythagorean theorem one is able to solve this issue with little to no issues. By simply substituting 5 and 15 for a and b (in the formula) we can obtain the result which will give us the necessary height of the ladder.
Therefore

<math> 5^2+15^2=250</math>

<math> \sqrt {250}= 15.8m </math>

15.8 is the exact height the ladder must be to fit the given parameters of the wall.

A third way to apply the pythagorean theorem is in computer games. As awkward as this game may be, it shows the integration of mathematics into the gaming world.
{{#ev:youtube | jQ2QDnpImcg | 400}}

[[User:MarcoGasparian|MarcoGasparian]]

=== What Can We Do With It?===

Various applications of the theorem should do here. There are plenty. I

=== What Does This Have To Do With the Trigonometric Circle?===

Given that the radius of a trigonometric circle is one, we can easily find out the sine length given the cosine length, or the reverse, using the Pythagorean theorem. This needs to be fleshed out with examples.

==Proposition for Basic Skills Project==

We propose to put up information about the Pythagorean Theorem. We could put up some proofs, various applications of the theorem, how to use it, and other such things. This could certainly tie in to distance and lines, as well, as getting the distance between two points on a graph is essentially the same thing.

[[User:BenJeffery|BenJeffery]]

----

Using information from the group members who responded (Christa, Marco, Ben):

==Things we all can do well==

10. Distance and Lines

12. Construction of Graphs

13a. Pythagorean Theorem

14. Areas and Volumes

15. Mathematical Writing

==Things some of us can do well==

3. Equations

4. Inequalities

5. Composition of Functions

8. Intersections of Functions

9. Reading Graphs of Functions

11. Operations on Graphs of Functions

13b. Trigonometry

== Things none of us can do well==

1. Basic Functions

2. Properties of Functions

6. Polynomial Long Division

7. Graphs of Functions

Course:MATH110/Archive/2010-2011/003/Groups/Group 17/Basic Skills Project

2010-12-02T17:11:31Z

ChristaBicego:

==The Pythagorean Theorem==

=== What Is It? ===
'''History:'''

Developed by a man named Pythagoras was born in the late 6th century B.C. on the island of Samos Greece. He proved that for any right hand triangle, the two shorter sides squared and added together exactly equal the squared amount of the longest side. This looks like:
a^2 + b^2 = c^2

'''Pythagorean Basics:'''

1) Only works for triangles

2) Only works for triangles with a right hand angle (90 degrees)

[[File:500px-Pythagorean.svg.png]]

This diagram demonstrates the use of pythagorean theorem to calculate the area of the square on the hypothenus- c. This is possible by summing the squared areas of the smaller sides - a and b

Christa Bicego

=== How Do We Know It's True? ===
[[User:BenJeffery|BenJeffery]]

There are many proofs of the theorem. One of the most straightforward is the following:

Take four right-angled triangles and connect them into a square as shown, so that they hypotenuses form an inner square as follows:

[[File:Proof_2.png]]

We can see that the length of each side of the outer square is <math>a+b</math>, and that the area must be <math>(a+b)^2</math>.

The pieces of the square are the inner square and our four triangles.

The area of each triangle can be given as <math>(1/2)ab</math>.

Meanwhile, the inner square has side length of <math>c</math>, and area of <math>c^2</math>.

From this, we can see that:

<math>(a+b)^2 = 2ab + c^2</math>

Expanding, we see that:

<math>a^2+2ab+b^2 = 2ab +c^2</math>

Balance the equation by subtracting <math>2ab</math> to get:

<math>a^2+b^2 = c^2</math>

This is, of course, the formula for the theorem!

If you prefer a more straight-forward visual proof, watch the following video. It clearly shows that the water in the two smaller squares (formed by squaring the length of the smaller sides) fits perfectly into the square formed from the hypotenuse.

{{#ev:youtube | CAkMUdeB06o | 400}}

=== How Do You Use It? ===

Explain how to apply the theorem to simple, as well as more complex examples. Verbal as well as mathematical examples are good.

Real-life application

There are many different real-life situations which involve the Pythagorean theorem.

For example, let’s assume two friends Fred and Matt want to meet at a specific point (ex: shopping mall). Fred is 8 Km away from the mall and Matt is 7 km away (assume they are at a right angle from each other in comparison to the mall), how do we find the distance between the two of them? By using the Pythagorean theorem we are able to determine the distance between them.

<math>5^2 + 7^2=74 </math>

<math>\sqrt {74} = 8.6 km </math>

8.6 is the distance that Fred and Matt are from each other

Another example of a real-life application of the Pythagorean theorem would be on how to figure out the necessary height of an object. Lets suppose you have a 15 meter high wall. You want to find out how long a ladder has to be if it is 5 meters from the base of the wall. Implementing the Pythagorean theorem one is able to solve this issue with little to no issues. By simply substituting 5 and 15 for a and b (in the formula) we can obtain the result which will give us the necessary height of the ladder.
Therefore

<math> 5^2+15^2=250</math>

<math> \sqrt {250}= 15.8m </math>

15.8 is the exact height the ladder must be to fit the given parameters of the wall.

A third way to apply the pythagorean theorem is in computer games. As awkward as this game may be, it shows the integration of mathematics into the gaming world.
{{#ev:youtube | jQ2QDnpImcg | 400}}

[[User:MarcoGasparian|MarcoGasparian]]

=== What Can We Do With It?===

Various applications of the theorem should do here. There are plenty. I

=== What Does This Have To Do With the Trigonometric Circle?===

Given that the radius of a trigonometric circle is one, we can easily find out the sine length given the cosine length, or the reverse, using the Pythagorean theorem. This needs to be fleshed out with examples.

==Proposition for Basic Skills Project==

We propose to put up information about the Pythagorean Theorem. We could put up some proofs, various applications of the theorem, how to use it, and other such things. This could certainly tie in to distance and lines, as well, as getting the distance between two points on a graph is essentially the same thing.

[[User:BenJeffery|BenJeffery]]

----

Using information from the group members who responded (Christa, Marco, Ben):

==Things we all can do well==

10. Distance and Lines

12. Construction of Graphs

13a. Pythagorean Theorem

14. Areas and Volumes

15. Mathematical Writing

==Things some of us can do well==

3. Equations

4. Inequalities

5. Composition of Functions

8. Intersections of Functions

9. Reading Graphs of Functions

11. Operations on Graphs of Functions

13b. Trigonometry

== Things none of us can do well==

1. Basic Functions

2. Properties of Functions

6. Polynomial Long Division

7. Graphs of Functions

Course:MATH110/Archive/2010-2011/003/Groups/Group 17/Basic Skills Project

2010-12-02T17:11:20Z

ChristaBicego:

==The Pythagorean Theorem==

=== What Is It? ===
'''History:'''

Developed by a man named Pythagoras was born in the late 6th century B.C. on the island of Samos Greece. He proved that for any right hand triangle, the two shorter sides squared and added together exactly equal the squared amount of the longest side. This looks like:
a^2 + b^2 = c^2

'''Pythagorean Basics:'''
1) Only works for triangles
2) Only works for triangles with a right hand angle (90 degrees)

[[File:500px-Pythagorean.svg.png]]

This diagram demonstrates the use of pythagorean theorem to calculate the area of the square on the hypothenus- c. This is possible by summing the squared areas of the smaller sides - a and b

Christa Bicego

=== How Do We Know It's True? ===
[[User:BenJeffery|BenJeffery]]

There are many proofs of the theorem. One of the most straightforward is the following:

Take four right-angled triangles and connect them into a square as shown, so that they hypotenuses form an inner square as follows:

[[File:Proof_2.png]]

We can see that the length of each side of the outer square is <math>a+b</math>, and that the area must be <math>(a+b)^2</math>.

The pieces of the square are the inner square and our four triangles.

The area of each triangle can be given as <math>(1/2)ab</math>.

Meanwhile, the inner square has side length of <math>c</math>, and area of <math>c^2</math>.

From this, we can see that:

<math>(a+b)^2 = 2ab + c^2</math>

Expanding, we see that:

<math>a^2+2ab+b^2 = 2ab +c^2</math>

Balance the equation by subtracting <math>2ab</math> to get:

<math>a^2+b^2 = c^2</math>

This is, of course, the formula for the theorem!

If you prefer a more straight-forward visual proof, watch the following video. It clearly shows that the water in the two smaller squares (formed by squaring the length of the smaller sides) fits perfectly into the square formed from the hypotenuse.

{{#ev:youtube | CAkMUdeB06o | 400}}

=== How Do You Use It? ===

Explain how to apply the theorem to simple, as well as more complex examples. Verbal as well as mathematical examples are good.

Real-life application

There are many different real-life situations which involve the Pythagorean theorem.

For example, let’s assume two friends Fred and Matt want to meet at a specific point (ex: shopping mall). Fred is 8 Km away from the mall and Matt is 7 km away (assume they are at a right angle from each other in comparison to the mall), how do we find the distance between the two of them? By using the Pythagorean theorem we are able to determine the distance between them.

<math>5^2 + 7^2=74 </math>

<math>\sqrt {74} = 8.6 km </math>

8.6 is the distance that Fred and Matt are from each other

Another example of a real-life application of the Pythagorean theorem would be on how to figure out the necessary height of an object. Lets suppose you have a 15 meter high wall. You want to find out how long a ladder has to be if it is 5 meters from the base of the wall. Implementing the Pythagorean theorem one is able to solve this issue with little to no issues. By simply substituting 5 and 15 for a and b (in the formula) we can obtain the result which will give us the necessary height of the ladder.
Therefore

<math> 5^2+15^2=250</math>

<math> \sqrt {250}= 15.8m </math>

15.8 is the exact height the ladder must be to fit the given parameters of the wall.

A third way to apply the pythagorean theorem is in computer games. As awkward as this game may be, it shows the integration of mathematics into the gaming world.
{{#ev:youtube | jQ2QDnpImcg | 400}}

[[User:MarcoGasparian|MarcoGasparian]]

=== What Can We Do With It?===

Various applications of the theorem should do here. There are plenty. I

=== What Does This Have To Do With the Trigonometric Circle?===

Given that the radius of a trigonometric circle is one, we can easily find out the sine length given the cosine length, or the reverse, using the Pythagorean theorem. This needs to be fleshed out with examples.

==Proposition for Basic Skills Project==

We propose to put up information about the Pythagorean Theorem. We could put up some proofs, various applications of the theorem, how to use it, and other such things. This could certainly tie in to distance and lines, as well, as getting the distance between two points on a graph is essentially the same thing.

[[User:BenJeffery|BenJeffery]]

----

Using information from the group members who responded (Christa, Marco, Ben):

==Things we all can do well==

10. Distance and Lines

12. Construction of Graphs

13a. Pythagorean Theorem

14. Areas and Volumes

15. Mathematical Writing

==Things some of us can do well==

3. Equations

4. Inequalities

5. Composition of Functions

8. Intersections of Functions

9. Reading Graphs of Functions

11. Operations on Graphs of Functions

13b. Trigonometry

== Things none of us can do well==

1. Basic Functions

2. Properties of Functions

6. Polynomial Long Division

7. Graphs of Functions

Course:MATH110/Archive/2010-2011/003/Groups/Group 17/Basic Skills Project

2010-12-02T17:07:43Z

ChristaBicego:

==The Pythagorean Theorem==

=== What Is It? ===
'''History:'''

Developed by a man named Pythagoras was born in the late 6th century B.C. on the island of Samos Greece. He proved that for any right hand triangle, the two shorter sides squared and added together exactly equal the squared amount of the longest side. This looks like:
a^2 + b^2 = c^2

Here we could describe the origin of the theorem, as well as the basic application.

[[File:500px-Pythagorean.svg.png]]

This diagram demonstrates the use of pythagorean theorem to calculate the area of the square on the hypothenus- c. This is possible by summing the squared areas of the smaller sides - a and b

Christa Bicego

=== How Do We Know It's True? ===
[[User:BenJeffery|BenJeffery]]

There are many proofs of the theorem. One of the most straightforward is the following:

Take four right-angled triangles and connect them into a square as shown, so that they hypotenuses form an inner square as follows:

[[File:Proof_2.png]]

We can see that the length of each side of the outer square is <math>a+b</math>, and that the area must be <math>(a+b)^2</math>.

The pieces of the square are the inner square and our four triangles.

The area of each triangle can be given as <math>(1/2)ab</math>.

Meanwhile, the inner square has side length of <math>c</math>, and area of <math>c^2</math>.

From this, we can see that:

<math>(a+b)^2 = 2ab + c^2</math>

Expanding, we see that:

<math>a^2+2ab+b^2 = 2ab +c^2</math>

Balance the equation by subtracting <math>2ab</math> to get:

<math>a^2+b^2 = c^2</math>

This is, of course, the formula for the theorem!

If you prefer a more straight-forward visual proof, watch the following video. It clearly shows that the water in the two smaller squares (formed by squaring the length of the smaller sides) fits perfectly into the square formed from the hypotenuse.

{{#ev:youtube | CAkMUdeB06o | 400}}

=== How Do You Use It? ===

Explain how to apply the theorem to simple, as well as more complex examples. Verbal as well as mathematical examples are good.

Real-life application

There are many different real-life situations which involve the Pythagorean theorem.

For example, let’s assume two friends Fred and Matt want to meet at a specific point (ex: shopping mall). Fred is 8 Km away from the mall and Matt is 7 km away (assume they are at a right angle from each other in comparison to the mall), how do we find the distance between the two of them? By using the Pythagorean theorem we are able to determine the distance between them.

<math>5^2 + 7^2=74 </math>

<math>\sqrt {74} = 8.6 km </math>

8.6 is the distance that Fred and Matt are from each other

Another example of a real-life application of the Pythagorean theorem would be on how to figure out the necessary height of an object. Lets suppose you have a 15 meter high wall. You want to find out how long a ladder has to be if it is 5 meters from the base of the wall. Implementing the Pythagorean theorem one is able to solve this issue with little to no issues. By simply substituting 5 and 15 for a and b (in the formula) we can obtain the result which will give us the necessary height of the ladder.
Therefore

<math> 5^2+15^2=250</math>

<math> \sqrt {250}= 15.8m </math>

15.8 is the exact height the ladder must be to fit the given parameters of the wall.

A third way to apply the pythagorean theorem is in computer games. As awkward as this game may be, it shows the integration of mathematics into the gaming world.
{{#ev:youtube | jQ2QDnpImcg | 400}}

[[User:MarcoGasparian|MarcoGasparian]]

=== What Can We Do With It?===

Various applications of the theorem should do here. There are plenty. I

=== What Does This Have To Do With the Trigonometric Circle?===

Given that the radius of a trigonometric circle is one, we can easily find out the sine length given the cosine length, or the reverse, using the Pythagorean theorem. This needs to be fleshed out with examples.

==Proposition for Basic Skills Project==

We propose to put up information about the Pythagorean Theorem. We could put up some proofs, various applications of the theorem, how to use it, and other such things. This could certainly tie in to distance and lines, as well, as getting the distance between two points on a graph is essentially the same thing.

[[User:BenJeffery|BenJeffery]]

----

Using information from the group members who responded (Christa, Marco, Ben):

==Things we all can do well==

10. Distance and Lines

12. Construction of Graphs

13a. Pythagorean Theorem

14. Areas and Volumes

15. Mathematical Writing

==Things some of us can do well==

3. Equations

4. Inequalities

5. Composition of Functions

8. Intersections of Functions

9. Reading Graphs of Functions

11. Operations on Graphs of Functions

13b. Trigonometry

== Things none of us can do well==

1. Basic Functions

2. Properties of Functions

6. Polynomial Long Division

7. Graphs of Functions

Course:MATH110/Archive/2010-2011/003/Groups/Group 17/Basic Skills Project

2010-12-02T17:04:09Z

ChristaBicego:

==The Pythagorean Theorem==

=== What Is It? ===
'''History:'''

Developed by a man named Pythagoras was born in the late 6th century B.C. on the island of Samos Greece. He proved that for any right hand triangle, the two shorter sides squared and added together exactly equal the squared amount of the longest side. This looks like:
a^2 + b^2 = c^2

Here we could describe the origin of the theorem, as well as the basic application.

[[File:500px-Pythagorean.svg.png]]

Christa Bicego

=== How Do We Know It's True? ===
[[User:BenJeffery|BenJeffery]]

There are many proofs of the theorem. One of the most straightforward is the following:

Take four right-angled triangles and connect them into a square as shown, so that they hypotenuses form an inner square as follows:

[[File:Proof_2.png]]

We can see that the length of each side of the outer square is <math>a+b</math>, and that the area must be <math>(a+b)^2</math>.

The pieces of the square are the inner square and our four triangles.

The area of each triangle can be given as <math>(1/2)ab</math>.

Meanwhile, the inner square has side length of <math>c</math>, and area of <math>c^2</math>.

From this, we can see that:

<math>(a+b)^2 = 2ab + c^2</math>

Expanding, we see that:

<math>a^2+2ab+b^2 = 2ab +c^2</math>

Balance the equation by subtracting <math>2ab</math> to get:

<math>a^2+b^2 = c^2</math>

This is, of course, the formula for the theorem!

If you prefer a more straight-forward visual proof, watch the following video. It clearly shows that the water in the two smaller squares (formed by squaring the length of the smaller sides) fits perfectly into the square formed from the hypotenuse.

{{#ev:youtube | CAkMUdeB06o | 400}}

=== How Do You Use It? ===

Explain how to apply the theorem to simple, as well as more complex examples. Verbal as well as mathematical examples are good.

Real-life application

There are many different real-life situations which involve the Pythagorean theorem.

For example, let’s assume two friends Fred and Matt want to meet at a specific point (ex: shopping mall). Fred is 8 Km away from the mall and Matt is 7 km away (assume they are at a right angle from each other in comparison to the mall), how do we find the distance between the two of them? By using the Pythagorean theorem we are able to determine the distance between them.

<math>5^2 + 7^2=74 </math>

<math>\sqrt {74} = 8.6 km </math>

8.6 is the distance that Fred and Matt are from each other

Another example of a real-life application of the Pythagorean theorem would be on how to figure out the necessary height of an object. Lets suppose you have a 15 meter high wall. You want to find out how long a ladder has to be if it is 5 meters from the base of the wall. Implementing the Pythagorean theorem one is able to solve this issue with little to no issues. By simply substituting 5 and 15 for a and b (in the formula) we can obtain the result which will give us the necessary height of the ladder.
Therefore

<math> 5^2+15^2=250</math>

<math> \sqrt {250}= 15.8m </math>

15.8 is the exact height the ladder must be to fit the given parameters of the wall.

A third way to apply the pythagorean theorem is in computer games. As awkward as this game may be, it shows the integration of mathematics into the gaming world.
{{#ev:youtube | jQ2QDnpImcg | 400}}

[[User:MarcoGasparian|MarcoGasparian]]

=== What Can We Do With It?===

Various applications of the theorem should do here. There are plenty. I

=== What Does This Have To Do With the Trigonometric Circle?===

Given that the radius of a trigonometric circle is one, we can easily find out the sine length given the cosine length, or the reverse, using the Pythagorean theorem. This needs to be fleshed out with examples.

==Proposition for Basic Skills Project==

We propose to put up information about the Pythagorean Theorem. We could put up some proofs, various applications of the theorem, how to use it, and other such things. This could certainly tie in to distance and lines, as well, as getting the distance between two points on a graph is essentially the same thing.

[[User:BenJeffery|BenJeffery]]

----

Using information from the group members who responded (Christa, Marco, Ben):

==Things we all can do well==

10. Distance and Lines

12. Construction of Graphs

13a. Pythagorean Theorem

14. Areas and Volumes

15. Mathematical Writing

==Things some of us can do well==

3. Equations

4. Inequalities

5. Composition of Functions

8. Intersections of Functions

9. Reading Graphs of Functions

11. Operations on Graphs of Functions

13b. Trigonometry

== Things none of us can do well==

1. Basic Functions

2. Properties of Functions

6. Polynomial Long Division

7. Graphs of Functions

Course:MATH110/Archive/2010-2011/003/Groups/Group 17/Basic Skills Project

2010-11-24T18:40:21Z

ChristaBicego:

==The Pythagorean Theorem==

=== What Is It? ===

Here we could describe the origin of the theorem, as well as the basic application.

[[File:500px-Pythagorean.svg.png]]

Christa Bicego

=== How Do We Know It's True? ===

Some different proofs of the theorem could go here.

Here's an interesting video proof to start off.

{{#ev:youtube | Z68uPQU2v3o | 400}}

=== How Do You Use It? ===

Explain how to apply the theorem to simple, as well as more complex examples. Verbal as well as mathematical examples are good.

=== What Can We Do With It?===

Various applications of the theorem should do here. There are plenty. I

=== What Does This Have To Do With the Trigonometric Circle?===

Given that the radius of a trigonometric circle is one, we can easily find out the sine length given the cosine length, or the reverse, using the Pythagorean theorem. This needs to be fleshed out with examples.

==Proposition for Basic Skills Project==

We propose to put up information about the Pythagorean Theorem. We could put up some proofs, various applications of the theorem, how to use it, and other such things. This could certainly tie in to distance and lines, as well, as getting the distance between two points on a graph is essentially the same thing.

[[User:BenJeffery|BenJeffery]]

----

Using information from the group members who responded (Christa, Marco, Ben):

==Things we all can do well==

10. Distance and Lines

12. Construction of Graphs

13a. Pythagorean Theorem

14. Areas and Volumes

15. Mathematical Writing

==Things some of us can do well==

3. Equations

4. Inequalities

5. Composition of Functions

8. Intersections of Functions

9. Reading Graphs of Functions

11. Operations on Graphs of Functions

13b. Trigonometry

== Things none of us can do well==

1. Basic Functions

2. Properties of Functions

6. Polynomial Long Division

7. Graphs of Functions

Course:MATH110/Archive/2010-2011/003/Groups/Group 17/Basic Skills Project

2010-11-12T05:32:39Z

ChristaBicego:

==Proposition for Basic Skills Project==

Guys - Any ideas for our basic skills project offer?
Seeing as we can apparently all do Distance and Lines well, how about we offer to do an overview with examples of that part?

It's pretty straight-forward, so there shouldn't be too many challenges with getting it together. If no one answers this by tonight, I'll just put it up as our offer.

Cheers,
[[User:BenJeffery|BenJeffery]]

looks good to me! i would be between that or the pythagorean theorem (just because it seems more interesting) but for me, either or work. [[User:MarcoGasparian|MarcoGasparian]]

I'm comfortable with doing either- leaning more to pythagorean theorem

[[User:ChristaBicego|ChristaBicego]]

----

Using information from the group members who responded (Christa, Marco, Ben):

==Things we all can do well==

10. Distance and Lines

12. Construction of Graphs

13a. Pythagorean Theorem

14. Areas and Volumes

15. Mathematical Writing

==Things some of us can do well==

3. Equations

4. Inequalities

5. Composition of Functions

8. Intersections of Functions

9. Reading Graphs of Functions

11. Operations on Graphs of Functions

13b. Trigonometry

== Things none of us can do well==

1. Basic Functions

2. Properties of Functions

6. Polynomial Long Division

7. Graphs of Functions

Course talk:MATH110/003/Groups/Group 17

2010-10-28T21:01:59Z

ChristaBicego:

==Basic Skills Knowledge==

Hey,

So, just put your names under everything that you have trouble with. If you are fine with it, leave it blank.
I'll format and post on our group page when it's filled in.

[[User:BenJeffery|BenJeffery]] 19:13, 28 October 2010 (UTC)

2.1 Basic functions

[[User:MarcoGasparian|MarcoGasparian]]

[[User:BenJeffery|BenJeffery]] (for Logarithmic functions)

Christa Bicego

2.2 Properties of functions

[[User:MarcoGasparian|MarcoGasparian]]

[[User:BenJeffery|BenJeffery]] (for Logarithmic functions)

Christa Bicego

2.3 Equations

[[User:MarcoGasparian|MarcoGasparian]]

[[User:BenJeffery|BenJeffery]] (Logarithms again!)

2.4 Inequalities

[[User:MarcoGasparian|MarcoGasparian]]

Christa Bicego

2.5 Composition of functions

[[User:MarcoGasparian|MarcoGasparian]]

2.6 Polynomial long division

[[User:MarcoGasparian|MarcoGasparian]]

[[User:BenJeffery|BenJeffery]] No clue

Christa Bicego

2.7 Graphs of functions

[[User:MarcoGasparian|MarcoGasparian]]

[[User:BenJeffery|BenJeffery]] (Mostly trigonometric/circles/etc...)

Christa Bicego

2.8 Intersections of functions

[[User:MarcoGasparian|MarcoGasparian]]

Christa Bicego

2.9 Reading graphs of functions

[[User:MarcoGasparian|MarcoGasparian]]

2.10 Distances and lines

2.11 Operations on graphs of functions

[[User:MarcoGasparian|MarcoGasparian]]

Christa Bicego

2.12 Construction of graphs

2.13 Trigonometry and the Pythagorean theorem

Christa Bicego (Trig)

2.14 Areas and volumes

2.15 Mathematical writing

==Comment on Homework 3==
Good job in getting most of the questions correct! But there are 10 missing....:( You've provided an organized and readable document, keep it up for the future! But next time, do all the questions, you can do them if you can do the 15 you did! For the very few you got wrong, if you've checked your answers, or read the question more carefully, you would have gotten right too! Also for number 2 a little bit more details on the thought process would be helpful.

[[User:JingFeiYu|JingFeiYu]]

----
So, I haven't really been able to find any properties specifically governing non-parallel quadrilaterals with two equal sides. The best I've been able to find is Bretschneider's Formula for finding the area of any quadrilateral. [http://2000clicks.com/MathHelp/GeometryTriangleAreaQuadrilateral.aspx]

Aside from that, there really don't seem to be any overarching properties. The problem seems to be that if we have no requirements aside from having 2 lengths be the same size, there are simply too many options. Any luck with you guys?

[[User:BenJeffery|BenJeffery]]

Hey guys, so I've been doing my 5 questions and have noticed that they are fairly theoretical in the sense of finding the solutions. I have various shapes and even timelines that I drem which I am fairly unsure how to possibly "draw" on this edit board. Is it alright if I just explain it here using only words?
marco

[[User:MarcoGasparian|MarcoGasparian]]

Yeah, I can only assume that it's okay to just answer in words, as opposed to images. One group did pretty impressive drawings on their page, but I don't think that that is really necessary. In fact, words might be better, since if you can say it clearly, then you understand it better...

[[User:BenJeffery|BenJeffery]]

alright cool! my post is up. feel free to make any adjustments on the equations or wording if you see any.
[[User:MarcoGasparian|MarcoGasparian]]

I'm going to move all our answers to the main page and sort them numerically. Hazeline and Avi, if you read this, please insert your answers in the appropriate areas.
[[User:BenJeffery|BenJeffery]]

==Problem 3==
hey guys, ive been giving a shot at question 3 but I have many doubts regarding the wording... in one of the situations, it states that Ed, Pascal Jason, the right fielder and the centre fielder are bachelors, the others are all married. however, Ed's sister is engaged to the second baseman. does this mean that I can consider the second baseman as married or as a bachelor?

also, consider these two statements:
Pascal and Charles each won $20 from the pitcher at a poker game,
Ed and the outfielders play cards during their free time,
I figured that this would imply that pascal and charles are both outfielders and that Ed is the pitcher. however, this is not the case.
The pitcher can't be Ed since Ed is a bachelor and it states that the pitcher has a wife.
The reason I also brought up Pascal and Charles is because from the previous statement it would seem as if pascal and charles are part of the outfieldiers. We are also told that "All the battery and infield except Charles, Hassan and Adam are shorter than Sung" nulling the fact that charles is an outfielder...

It also states that Sung is in the process of getting divorced. once again can I consider him a bachelor or married? if I still consider him as married. what is the importance of that phrase in the context of the question?
I am extremely confused as to how to take on this question.

If someone could look at it id greatly appreciate it.
Thx

[[User:MarcoGasparian|MarcoGasparian]]

== '''Question 1''' ==

A bus traveled from the terminal to the airport at an average speed of 30 mi/hr and the trip tok one hour and 20 minutes. The bus traveled from the airport back to the terminal and again average speed was 30 mi/hr. however, the return trip required 80 mins. Explain
'''Step 1: Understand the problem:'''

The problem is asking to explain the difference between the trip to the airport and the return trip from the airport.

-Terminal to Airport= one hour 20 minutes at 30 mi/hr

- Airport to terminal= 80 minutes at 30 mi/hour

'''Step 2: Plan a strategy for solving the problem:'''

First: convert time into same units

Second: Compare distance between two trips (a)

Third: Compare time between two trips (b)

Fourth: Compare speed between two trips (c)

- If two of a, b, c are the comparably the same, that means the remaining must be equal as well (Pythagorean Theory)

'''Step 3: Execute Strategy'''

one hour= 60 minutes

one hour 20 minutes = 60 +20 = 80 minutes

80 minutes = 80 minutes

a) compare distances,

- Airport to terminal

- terminal to airport

=Same distance

b) After conversion, realized that they are the same time spent traveling

c)speed= average 30mi/hr both trips

'''Step 4: Check'''

- Because the distance and speed were the same in both trips, so is the time

- The time had to be converted to same units for clear view that they were both the same traveling time

== '''Question 6:''' ==

Three kinds of apples are all mixed up in a basket. How many apples must you draw (w/out looking) from the basket to be sure of getting at least 2 of one kind?

'''Step 1: Understand the problem'''

- There are three kinds of DIFFERENT apples- how many times does it take of pulling one apple out at a time to randomly get 2 of the same kind.

- There is three kind: gala, pink lady, and spartan

- How many times do I have to stick my hand in the basket to get 2 galas, or 2 pink ladys, or 2 spartans

'''Step 2: Plan a Strategy:'''

-denote g to gala, p to pink lady, and s to spartan to represent the three types of apples in the basket

-Imagination testing

Step 3: Execute Strategy

- Three types of apples, must have at least 3 pulls to ensure you get a duplicate

- so, 3 + x would be the equation

- first pull: g, second pull: p, third pull: s, fourth pull s

- You must pull more than 3 time times to be sure you will receive two of the same kind

-The min. is 4

'''Step 4: Check'''
- One must pull at least 4 times to ensure they will receive two of the same kind

== '''Question 11''' ==
A woman, her older brother, her son, and her daughter are chess players. The worst player’s twin, who is one of the four players, and the best player are of opposite sex. The worst player and the best player have the same age. If this is possible, who is the worst player?

'''Step 1: Understand the problem'''

- out of the sequence of 4 individuals playing chess. Who is the worst player and best player?

-Age sequence: woman's older brother, woman, women's son and daughter (same age)

-only two people at table have the same age and can only have the same age.

'''Step 2: Plan a Strategy:'''

-denote w for women, b for her older brother, s for her son and d for her daughter

- b- w= greater than 0

- s-d= 0

-worst player's twin(is a player) = opposite sex of best player

-worst player(girl), twin(girl,boy)= best player (boy, girl)

'''Step 3: Execute'''

- The worst players twin cannot be the best player

- the only 2 people who can have the same age of the four players is the daughter and son

- This is not possible because the worst player, twin and best player would have to be triplets

-but they are not because they are referred to as twin and not one of a triplets

'''Step 4: Check'''

- This problem is not possible because no player is of the same age expect the possibility that the daughter and son could be twins

- However, the wording of the problem determines that they cannot be twins because one of them already has a twin

== '''Question 16''' ==

Suppose that each daughter in your family has the same number of brothers as she has sisters, and each son in your family has twice as many sisters as he has brothers. How many sons and daughters are in the family?

'''Step 1: Understand the problem'''

- each daughter in the family has the same number of brothers as she has sisters

-Sisters= brothers

- each son has twice as many sisters as he has brothers

- 2(brothers)= sisters

- How many sons and daughters are in the family?

'''Step 2: Plan a strategy'''

- Test numbers that follow the brothers to sisters pattern above

'''Step 3: Execute:'''

- If Daughter 1 has 2 sisters she must have 2 brothers, however this means that the son 1 has 1 brothers have 3 sisters= does not work because brothers must have double the amount of sisters than brothers. Not correct.

- if daughter 1 has 3 sisters she must have 3 brothers. Son 1 therefore has 2 brothers and 4 sisters. This is correct because:

'''Step 4: test'''
- if daughter 1 has 3 sisters she must have 3 brothers. Son 1 therefore has 2 brothers and 4 sisters. This is correct because:

- Each daughter has 3 sisters and 3 brothers ( same number of sisters as brothers). Also each son has 2 brothers and 4 sisters ( double as many sisters as brothers).

== '''Question 21''' ==

Sven placed exactly in the middle among all runners in a race. Dan was slower than Sven, in 10th place, and Lars was in 16th place. How many runners were in the race?

'''Step 1: understand the problem'''

-Sven is exactly in the middle of the runners in the race

-Dan was slower than Sven (10th place)

-Lars in 16th place

- Sven is between 1st and 9th place

- How many total runners were in the race?

- Sven place is half the amount of runners in the race

- There are more than 16 runners

'''Step 2: plan strategy'''

- eliminate some options of Svens placement by multipling by two (places 1 through 9) and eliminating those that do not equal greater than 16 (lars place)

-Because Sven is exactly in the middle, the total number must be odd. So, 2 x Svens postive - 1 will be the total number of runners in the race

'''Step 3: Execute'''

- 1x2= 2

-2x2=4

-2x3=6

-2x4= 8

-2x5=10 (dans place)

-2x6=12

-2x7=14

-2x8= 16 (Lars place)

-2x9= 18 (The only place Sven could be that multiplied by 2 equal greater than lars place)

-18- 1 = 17

'''Step 4: Check'''

- There are 17 people in the race in total because Sven is in 9th place and exactly in the middle of the runners

==Question 3==

3. One of three boxes contains apples, another box contains oranges, and another box contains a mixture of apples and oranges. The boxes are labeled APPLES, ORANGES and APPLES AND ORANGES, but each label is incorrect. Can you select one fruit from only one box and determine the correct labels? Explain.

Step 1: There are 3 different variations of fruits in the boxes. Apples (A), Oranges (O), and Apples + Oranges (A+O)
Every box IS mislabeled with a different fruit (this is key). Therefore, apples might be oranges, or apples and oranges. Oranges might be labeled as apples etc...

Step 2:
You are given the option to pick ONE (it doesn’t matter which one) of the boxes and know the label it has as well as the content inside it.

Step 3:
With step 2 in mind lets suppose we pick the box labeled as oranges. Now, lets assume that the box labeled as oranges then has apples inside it.
Now, think about this for a minute… if we chose a box labeled as oranges, there are two labels left, apples and apples + oranges.
We know for a fact that every single box is mislabeled. Therefore, the content of a box labeled as apples can’t contain apples in it. Which means that the only possible box that could contain apples is the box labeled as apples + oranges, and the remainder is the box labeled as apples contains apples + oranges.

Step 4: lets look at another ex: Lets assume we picked the box labeled as apples, we open the box and see it contains oranges. once again from this we can derive that the box labeled as oranges will not in fact contain oranges as it goes against the rules which were previously established by the question. Therefore since the only remaining box is apples + oranges, we can assume that apples will be in that box and apples + oranges will be in the box labeled as oranges.
[[User:MarcoGasparian|MarcoGasparian]]

==Question 8==

8. Reuben says, “Two days ago I was 20 years old. Later next year I will be 23 years old.” Explain how this is possible.

Step 1: The most important aspect of how this question was written is the fact that they state TWO days ago and not one. This means that one day ago Reuben could already be 21 (keep this in mind).

Step 2: The easiest form to solve this problem is to draw a timeline. Given that it is difficult to draw an accurate timeline I will simply draw a table
Lets assume that:
T=Today
T-1= One day ago
T-2= Two days ago
T+ one year later-1= one year later -1 day (December 31st 2010)
T+ two years later – 1 day= two years later – day (December 31st 2011)

Step 3:

Lets assume that T= January 1st of 2010
And that Reuben’s B-day was December 31st= T-1 He turned 21 on 2009
And that on December 30th = T-2 Reuben was still 20 since he turned 21 on December 31st.
With that in mind if we simply use logic than in T+ one year – 1 day would be December 31st of 2010 and Reuben would be celebrating his 22nd birthday. This however is still in 2010 which is the same year. The question states “later next year I will be 23 years old” Therefore, in the year 2011 on December 31st Reuben will be celebrating his 23rd birthday.

Step 4: Think of this question in terms of formulas
If Reuben’s B-day is on December 31st = T-1 we are going back an entire year from 2010= T to 2009= T-1
And the difference in years between T and T + two years later -1 day is also 2 years
Therefore the difference between
T-1 and T+ two years later – 1 day is 3 Years which is between Reuben being 20 to 23 years old.
[[User:MarcoGasparian|MarcoGasparian]]

==Question 13==

13. If a clock takes 5 seconds to strike 5:00 (with 5 equally spaced chimes), how long does it take to strike 10:00 (with 10 equally spaced chimes)?

Step 1: At first glance this question may seem like the obvious answer is 10 (I thought so). However, we must take into consideration that every chime is divided by little halts of the noise the clock makes. In this instance it will make 5 chimes in a period of 5 seconds. We are being asked how long it will take to make 10 chimes taking the halts into consideration.

Step 2: The easiest way to answer this question is by drawing a timeline by evenly distributing 5 chimes throughout it and 10 chimes through the second timeline:

(.)= chimes
(_)= halts

5 second 5:00 chime

.____.____.____.____.

10:00 chime
.___.___.___.___.___.___.___.___.___.

Step 3:
The question stated that it would take the clock 5 seconds to complete 5 chimes with the halts in between them therefore by looking at the graph we observe that it takes 5 chimes/ 4 halts in between each chime. Which means 5/4=1.25 halts between each chime. 1.25*4= 5 seconds

Using the same concept with the 10 chimes. We count the number of halts and see that there are 9. Since we already know that the number of seconds it took between each chime is 1.25, we use the formula 9/4=2.25 seconds 2.25*5= 11.25 seconds

Step 4: In order to prove this lets assume try to figure out what would happen if it were 20 chimes.

.__.__.__.__.__.__.__.__.__.__.__.__.__.__.__.__.__.__.__.

19/4= 4.75 seconds 4.75*5= 23.75 seconds
[[User:MarcoGasparian|MarcoGasparian]]

==Question 18==

18. Alice takes one-third of the pennies from a large jar. Then Bret takes one-third of the remaining pennies from the jar. Finally, Carla takes one-third of the remaining pennies from the jar, leaving 40 pennies in the jar. How many pennies were in the jar at the start?

Step 1: The key concept to grasp in this particular question is that the 1/3 that Bret and Carla are taking are the REMAINDER of what had been left at the jar based on what had already been removed. Nevertheless, Alice, Bret, and Carla are all taking 1/3 of what is being offered to them.

Step 2: In order to figure out this problem you must think backwards, working from the solution. The question which I posed in my own mind was what equals 40 if its has 1/3 of it subtracted 3 times

Step 3: I looked at the number 40 and started testing different possibilities with numbers whose value of 1/3 was still an integer. I then realized that 60*1/3 = 20
60-20=40

20= The amount Carla took from the 60 Remainder from the 1/3 Alice took and then the 1/3 that Bret took (after Alice).

I repeated the process and realized that
90*1/3= 30
90-30= 60
30= Amount Bret took from the 90 remainder of the 1/3 Alice took.

I finally did the process a third time and realized that

135*1/3= 45
135-45=90
45= Amount Alice took from the TOTAL = 135
How many pennies were in the jar at the start? 135 pennies

Step 4: When I looked at the questions solution, I noticed that there was a pattern with the formula I was using.

Essentially the amount that remained was twice as much as the value a person had previously taken. This makes sense since we are subtracting 1/3 of the 3/3 leaving us with 2/3
(2/3)/(1/3)= 2 for every 1

[[User:MarcoGasparian|MarcoGasparian]]

==Question 23==
23. Suppose you overhear the following conversation: Paul: How old are your three children? Paula: The product of their ages is 36 and the sum of their ages is the same as today's date. Paul: That is not enough information. Paula: The oldest child also has red hair. If you were Paul could you determine the ages of Paula's children? Explain.

Step 1:In order to figure out this question I eliminated the useless information. The fact that the oldest child has red hair is a null point. I then formulated different possibilities in my head of what could be done if I were to try to solve this.

Step 2: I realized that the easiest way to figure out this problem is to create a factor tree of 36. 36 can be factored to 36*1, 2*18, 3*12, 4*9, 6*6, 4*3*3, 2*3*6, 2*2*3*3, 2*3*6 Note that the only possible answers were the ones that could be factored into 3 different numbers as there are exactly 3 children.

Step 3: The question also states that the sum was today’s date. Since today is the 12th, the only factor which would be possible is 2*3*6
Since the product of that equals 36 and the sum equals 12. Also, it could not have been 6*6 since it was asking for 3 children and not 2

Step 4: In order to check this I tried all different factors of 36 and saw through trial and error that this was the only compatible one.
[[User:MarcoGasparian|MarcoGasparian]]

Course:MATH110/Archive/2010-2011/003/Groups/Group 17/Problem Solving 2

2010-10-19T23:58:38Z

ChristaBicego:

== Problem Set 2==

===Question 1===
Question 1: Five persons named their pets after each other. From the following clues, can you decide which pet belongs to Suzan's mother? Tosh owns a cat, Bianca owns a frog that she loves, Jaela owns a parrot which keeps calling her "darling, darling", Jun owns a snake, don't mess with him, Suzan is the name of the frog, The cat is named Jun, The name by which they call the turtle is the name of the woman whose pet is Tosh, Finally, Suzan's mother's pet is Bianca.
The question is asking, which pet belongs to Suzan's mother?
- we can figure this out by connecting the names of the different pets to their owners as the pets are all named after these individuals
First: the info from the question:
Tosh has a cat named Jun Bianca has a frog named Susan Jaela has a parot named - ? Jun has a snake named ? Suzans owns a turtle named ?
Suzans mother cannot be susan(susans mother cannot be her daughter...), or Bianca (Susan's mother's pet name is Bianca)
Tosh has a cat named Jun Bianca has a frog named Susan Jaela has a parot named - (Bianca or Tosh) Jun has a snake named (Jaela, Bianca or Susan) Suzans owns a turtle named (Tosh or Jaela)
The only way the question satisfies all points is if :
Tosh has a cat named Jun Bianca has a frog named Susan Jaela has a parot named - Tosh Jun has a snake named Bianca Suzans owns a turtle named Jaela
Therefore: Susans mother is Jun and she owns a snake

===Question 2===
''Bohao, Stewart, Dylan, Tim and Chan are the five players of a basketball team. Two are left handed and three right handed, Two are over 2m tall and three are under 2m, Bohao and Dylan are of the same handedness, whereas Tim and Chan use different hands. Stewart and Chan are of the same height range, while Dylan and Tim are in different height ranges. If you know that the one playing centre is over 2m tall and is left handed, can you guess his name?''

So, we need to find out who on the team is over 2m tall and left-handed.

Looking at the information about the players, we see that there are 3 right-handers and two left-handers. We know that Bohao and Dylan are the same handedness, while Tim and Chan are different. This tells us that either Tim or Chan have the same handedness as both Bohao and Dylan. This means that Bohao and Dylan must be right-handed, since they are in a group of 3 people that share the same hand.

Looking at height, we can use the same deduction. There are three people under 2m tall and two over 2m tall. If Stewart and Chan are of the same size, and Dylan and Tim are different, then we know that Stewart and Chan are in a group of three people, and therefore must be under 2m tall.

Finally, we need someone who is over 2m and left-handed. Bohao and Dylan are out, since they are right-handed. Chan and Stewart are out, since they are under 2m tall. From the list of 5 players, the only remaining player is Tim. Therefore, Tim is our centerman.

[[User:BenJeffery|BenJeffery]]

===Question 3===
Adam, Bobo, Charles, Ed, Hassan, Jason, Mathieu, Pascal and Sung have formed a baseball team. The following facts are true:

Adam does not like the catcher,
Ed's sister is engaged to the second baseman,
The centre fielder is taller than the right fielder,
Hassan and the third baseman live in the same building,
Pascal and Charles each won $20 from the pitcher at a poker game,
Ed and the outfielders play cards during their free time,
The pitcher's wife is the third baseman's sister,
All the battery and infield except Charles, Hassan and Adam are shorter than Sung,
Pascal, Adam and the shortstop lost $100 each at the race track,
The second baseman beat Pascal, Hassan, Bobo and the catcher at billiards,
Sung is in the process of getting a divorce,
The catcher and the third baseman each have two legitimate children,
Ed, Pascal Jason, the right fielder and the centre fielder are bachelors, the others are all married
The shortstop, the third baseman and Bobo all attended the fight,
Mathieu is the shortest player of the team,
Determine the positions of each player on the baseball team.

Note: On a baseball team there are three outfielders (right, centre and left), four infielders (first baseman, second baseman, third baseman and shortstop) and the battery (pitcher and catcher).

{| border="1"
|
|Adam
|Bobo
|Charles
|Ed
|Hassan
|Jason
|Mathieu
|Pascal
|Sung
|-
|Right Outfielder
|x
|x
|x
|x
|x
|x
|o
|x
|x
|-
|Center Outfielder
|x
|o
|x
|x
|x
|x
|x
|x
|x
|-
|Left Outfielder
|x
|x
|x
|x
|x
|x
|x
|x
|o
|-
|1st Baseman
|x
|x
|x
|x
|x
|x
|x
|o
|x
|-
|2nd Baseman
|x
|x
|x
|x
|x
|o
|x
|x
|x
|-
|3rd Baseman
|o
|x
|x
|x
|x
|x
|x
|x
|x
|-
|Shortstop
|x
|x
|x
|o
|x
|x
|x
|x
|x
|-
|Pitcher
|x
|x
|x
|x
|o
|x
|x
|x
|x
|-
|Catcher
|x
|x
|o
|x
|x
|x
|x
|x
|x
|}

The graph above depicts with "x's" and "o's" the correct placement of each player on the baseball field. "X" being were they aren't and "o" being where they are...obviously.

Here are some of the facts that I derived from the statements the question gave us to come up with an answer.

Hassan is not the third baseman because he lives with the third baseman.

Ed is not the 2nd baseman because his sister is engaged to the second baseman.

Adam is not the catcher because he does not like the catcher.

Mathieu is not the center fielder because the center fielder is taller than the right fielder.
Mathieu is the shortest of them all.

Pitcher has wife, therefore it can’ t be Ed, Pascal Jason, the right fielder and the centre
fielder

Pascal and Adam aren’ t shortstop because both of them and the shortstop lost 100$ at the
race track

Pascal, Hassan, Bobo cant be the second baseman or catcher because the second baseman
beat Pascal, Hassan, Bobo, and the catcher at billiards

All the battery and infield except Charles, Hassan and Adam are shorter than Sung,
Therefore, Charles, Hassan, and Adam are either battery or infield

Pascal and Charles can’ t be the pitcher because they won money from him at a poker
game

Ed can’ t be an outfielder because he plays cards with them

This list would go on and on, but you get the idea.
[[User:MarcoGasparian|MarcoGasparian]]
===Question 4===

===Question 5===

Course talk:MATH110/003/Groups/Group 17/Problem Solving 2

2010-10-19T23:57:10Z

ChristaBicego: Created page with 'Question 1: Five persons named their pets after each other. From the following clues, can you decide which pet belongs to Suzan's mother? Tosh owns a cat, Bianca owns a frog that…'

Question 1:
Five persons named their pets after each other. From the following clues, can you decide which pet belongs to Suzan's mother?
Tosh owns a cat,
Bianca owns a frog that she loves,
Jaela owns a parrot which keeps calling her "darling, darling",
Jun owns a snake, don't mess with him,
Suzan is the name of the frog,
The cat is named Jun,
The name by which they call the turtle is the name of the woman whose pet is Tosh,
Finally, Suzan's mother's pet is Bianca.

The question is asking, which pet belongs to Suzan's mother?

- we can figure this out by connecting the names of the different pets to their owners as the pets are all named after these individuals

First: the info from the question:

Tosh has a cat named Jun
Bianca has a frog named Susan
Jaela has a parot named - ?
Jun has a snake named ?
Suzans owns a turtle named ?

Suzans mother cannot be susan(susans mother cannot be her daughter...), or Bianca (Susan's mother's pet name is Bianca)

Tosh has a cat named Jun
Bianca has a frog named Susan
Jaela has a parot named - (Bianca or Tosh)
Jun has a snake named (Jaela, Bianca or Susan)
Suzans owns a turtle named (Tosh or Jaela)

The only way the question satisfies all points is if :

Tosh has a cat named Jun
Bianca has a frog named Susan
Jaela has a parot named - Tosh
Jun has a snake named Bianca
Suzans owns a turtle named Jaela

Therefore: Susans mother is Jun and she owns a snake

Course talk:MATH110/003/Groups/Group 17

2010-10-13T02:36:44Z

ChristaBicego:

----
So, I haven't really been able to find any properties specifically governing non-parallel quadrilaterals with two equal sides. The best I've been able to find is Bretschneider's Formula for finding the area of any quadrilateral. [http://2000clicks.com/MathHelp/GeometryTriangleAreaQuadrilateral.aspx]

Aside from that, there really don't seem to be any overarching properties. The problem seems to be that if we have no requirements aside from having 2 lengths be the same size, there are simply too many options. Any luck with you guys?

[[User:BenJeffery|BenJeffery]]

Hey guys, so I've been doing my 5 questions and have noticed that they are fairly theoretical in the sense of finding the solutions. I have various shapes and even timelines that I drem which I am fairly unsure how to possibly "draw" on this edit board. Is it alright if I just explain it here using only words?
marco

[[User:MarcoGasparian|MarcoGasparian]]

Yeah, I can only assume that it's okay to just answer in words, as opposed to images. One group did pretty impressive drawings on their page, but I don't think that that is really necessary. In fact, words might be better, since if you can say it clearly, then you understand it better...

[[User:BenJeffery|BenJeffery]]

alright cool! my post is up. feel free to make any adjustments on the equations or wording if you see any.
[[User:MarcoGasparian|MarcoGasparian]]

== '''Question 1''' ==

A bus traveled from the terminal to the airport at an average speed of 30 mi/hr and the trip tok one hour and 20 minutes. The bus traveled from the airport back to the terminal and again average speed was 30 mi/hr. however, the return trip required 80 mins. Explain
'''Step 1: Understand the problem:'''

The problem is asking to explain the difference between the trip to the airport and the return trip from the airport.

-Terminal to Airport= one hour 20 minutes at 30 mi/hr

- Airport to terminal= 80 minutes at 30 mi/hour

'''Step 2: Plan a strategy for solving the problem:'''

First: convert time into same units

Second: Compare distance between two trips (a)

Third: Compare time between two trips (b)

Fourth: Compare speed between two trips (c)

- If two of a, b, c are the comparably the same, that means the remaining must be equal as well (Pythagorean Theory)

'''Step 3: Execute Strategy'''

one hour= 60 minutes

one hour 20 minutes = 60 +20 = 80 minutes

80 minutes = 80 minutes

a) compare distances,

- Airport to terminal

- terminal to airport

=Same distance

b) After conversion, realized that they are the same time spent traveling

c)speed= average 30mi/hr both trips

'''Step 4: Check'''

- Because the distance and speed were the same in both trips, so is the time

- The time had to be converted to same units for clear view that they were both the same traveling time

== '''Question 6:''' ==

Three kinds of apples are all mixed up in a basket. How many apples must you draw (w/out looking) from the basket to be sure of getting at least 2 of one kind?

'''Step 1: Understand the problem'''

- There are three kinds of DIFFERENT apples- how many times does it take of pulling one apple out at a time to randomly get 2 of the same kind.

- There is three kind: gala, pink lady, and spartan

- How many times do I have to stick my hand in the basket to get 2 galas, or 2 pink ladys, or 2 spartans

'''Step 2: Plan a Strategy:'''

-denote g to gala, p to pink lady, and s to spartan to represent the three types of apples in the basket

-Imagination testing

Step 3: Execute Strategy

- Three types of apples, must have at least 3 pulls to ensure you get a duplicate

- so, 3 + x would be the equation

- first pull: g, second pull: p, third pull: s, fourth pull s

- You must pull more than 3 time times to be sure you will receive two of the same kind

-The min. is 4

'''Step 4: Check'''
- One must pull at least 4 times to ensure they will receive two of the same kind

== '''Question 11''' ==
A woman, her older brother, her son, and her daughter are chess players. The worst player’s twin, who is one of the four players, and the best player are of opposite sex. The worst player and the best player have the same age. If this is possible, who is the worst player?

'''Step 1: Understand the problem'''

- out of the sequence of 4 individuals playing chess. Who is the worst player and best player?

-Age sequence: woman's older brother, woman, women's son and daughter (same age)

-only two people at table have the same age and can only have the same age.

'''Step 2: Plan a Strategy:'''

-denote w for women, b for her older brother, s for her son and d for her daughter

- b- w= greater than 0

- s-d= 0

-worst player's twin(is a player) = opposite sex of best player

-worst player(girl), twin(girl,boy)= best player (boy, girl)

'''Step 3: Execute'''

- The worst players twin cannot be the best player

- the only 2 people who can have the same age of the four players is the daughter and son

- This is not possible because the worst player, twin and best player would have to be triplets

-but they are not because they are referred to as twin and not one of a triplets

'''Step 4: Check'''

- This problem is not possible because no player is of the same age expect the possibility that the daughter and son could be twins

- However, the wording of the problem determines that they cannot be twins because one of them already has a twin

== '''Question 16''' ==

Suppose that each daughter in your family has the same number of brothers as she has sisters, and each son in your family has twice as many sisters as he has brothers. How many sons and daughters are in the family?

'''Step 1: Understand the problem'''

- each daughter in the family has the same number of brothers as she has sisters

-Sisters= brothers

- each son has twice as many sisters as he has brothers

- 2(brothers)= sisters

- How many sons and daughters are in the family?

'''Step 2: Plan a strategy'''

- Test numbers that follow the brothers to sisters pattern above

'''Step 3: Execute:'''

- If Daughter 1 has 2 sisters she must have 2 brothers, however this means that the son 1 has 1 brothers have 3 sisters= does not work because brothers must have double the amount of sisters than brothers. Not correct.

- if daughter 1 has 3 sisters she must have 3 brothers. Son 1 therefore has 2 brothers and 4 sisters. This is correct because:

'''Step 4: test'''
- if daughter 1 has 3 sisters she must have 3 brothers. Son 1 therefore has 2 brothers and 4 sisters. This is correct because:

- Each daughter has 3 sisters and 3 brothers ( same number of sisters as brothers). Also each son has 2 brothers and 4 sisters ( double as many sisters as brothers).

== '''Question 21''' ==

Sven placed exactly in the middle among all runners in a race. Dan was slower than Sven, in 10th place, and Lars was in 16th place. How many runners were in the race?

'''Step 1: understand the problem'''

-Sven is exactly in the middle of the runners in the race

-Dan was slower than Sven (10th place)

-Lars in 16th place

- Sven is between 1st and 9th place

- How many total runners were in the race?

- Sven place is half the amount of runners in the race

- There are more than 16 runners

'''Step 2: plan strategy'''

- eliminate some options of Svens placement by multipling by two (places 1 through 9) and eliminating those that do not equal greater than 16 (lars place)

-Because Sven is exactly in the middle, the total number must be odd. So, 2 x Svens postive - 1 will be the total number of runners in the race

'''Step 3: Execute'''

- 1x2= 2

-2x2=4

-2x3=6

-2x4= 8

-2x5=10 (dans place)

-2x6=12

-2x7=14

-2x8= 16 (Lars place)

-2x9= 18 (The only place Sven could be that multiplied by 2 equal greater than lars place)

-18- 1 = 17

'''Step 4: Check'''

- There are 17 people in the race in total because Sven is in 9th place and exactly in the middle of the runners

==Question 3==

3. One of three boxes contains apples, another box contains oranges, and another box contains a mixture of apples and oranges. The boxes are labeled APPLES, ORANGES and APPLES AND ORANGES, but each label is incorrect. Can you select one fruit from only one box and determine the correct labels? Explain.

Step 1: There are 3 different variations of fruits in the boxes. Apples (A), Oranges (O), and Apples + Oranges (A+O)
Every box IS mislabeled with a different fruit (this is key). Therefore, apples might be oranges, or apples and oranges. Oranges might be labeled as apples etc...

Step 2:
You are given the option to pick ONE (it doesn’t matter which one) of the boxes and know the label it has as well as the content inside it.

Step 3:
With step 2 in mind lets suppose we pick the box labeled as oranges. Now, lets assume that the box labeled as oranges then has apples inside it.
Now, think about this for a minute… if we chose a box labeled as oranges, there are two labels left, apples and apples + oranges.
We know for a fact that every single box is mislabeled. Therefore, the content of a box labeled as apples can’t contain apples in it. Which means that the only possible box that could contain apples is the box labeled as apples + oranges, and the remainder is the box labeled as apples contains apples + oranges.

Step 4: lets look at another ex: Lets assume we picked the box labeled as apples, we open the box and see it contains oranges. once again from this we can derive that the box labeled as oranges will not in fact contain oranges as it goes against the rules which were previously established by the question. Therefore since the only remaining box is apples + oranges, we can assume that apples will be in that box and apples + oranges will be in the box labeled as oranges.
[[User:MarcoGasparian|MarcoGasparian]]

==Question 8==

8. Reuben says, “Two days ago I was 20 years old. Later next year I will be 23 years old.” Explain how this is possible.

Step 1: The most important aspect of how this question was written is the fact that they state TWO days ago and not one. This means that one day ago Reuben could already be 21 (keep this in mind).

Step 2: The easiest form to solve this problem is to draw a timeline. Given that it is difficult to draw an accurate timeline I will simply draw a table
Lets assume that:
T=Today
T-1= One day ago
T-2= Two days ago
T+ one year later-1= one year later -1 day (December 31st 2010)
T+ two years later – 1 day= two years later – day (December 31st 2011)

Step 3:

Lets assume that T= January 1st of 2010
And that Reuben’s B-day was December 31st= T-1 He turned 21 on 2009
And that on December 30th = T-2 Reuben was still 20 since he turned 21 on December 31st.
With that in mind if we simply use logic than in T+ one year – 1 day would be December 31st of 2010 and Reuben would be celebrating his 22nd birthday. This however is still in 2010 which is the same year. The question states “later next year I will be 23 years old” Therefore, in the year 2011 on December 31st Reuben will be celebrating his 23rd birthday.

Step 4: Think of this question in terms of formulas
If Reuben’s B-day is on December 31st = T-1 we are going back an entire year from 2010= T to 2009= T-1
And the difference in years between T and T + two years later -1 day is also 2 years
Therefore the difference between
T-1 and T+ two years later – 1 day is 3 Years which is between Reuben being 20 to 23 years old.
[[User:MarcoGasparian|MarcoGasparian]]

==Question 13==

13. If a clock takes 5 seconds to strike 5:00 (with 5 equally spaced chimes), how long does it take to strike 10:00 (with 10 equally spaced chimes)?

Step 1: At first glance this question may seem like the obvious answer is 10 (I thought so). However, we must take into consideration that every chime is divided by little halts of the noise the clock makes. In this instance it will make 5 chimes in a period of 5 seconds. We are being asked how long it will take to make 10 chimes taking the halts into consideration.

Step 2: The easiest way to answer this question is by drawing a timeline by evenly distributing 5 chimes throughout it and 10 chimes through the second timeline:

(.)= chimes
(_)= halts

5 second 5:00 chime

.____.____.____.____.

10:00 chime
.___.___.___.___.___.___.___.___.___.

Step 3:
The question stated that it would take the clock 5 seconds to complete 5 chimes with the halts in between them therefore by looking at the graph we observe that it takes 5 chimes/ 4 halts in between each chime. Which means 5/4=1.25 halts between each chime. 1.25*4= 5 seconds

Using the same concept with the 10 chimes. We count the number of halts and see that there are 9. Since we already know that the number of seconds it took between each chime is 1.25, we use the formula 9/4=2.25 seconds 2.25*5= 11.25 seconds

Step 4: In order to prove this lets assume try to figure out what would happen if it were 20 chimes.

.__.__.__.__.__.__.__.__.__.__.__.__.__.__.__.__.__.__.__.

19/4= 4.75 seconds 4.75*5= 23.75 seconds
[[User:MarcoGasparian|MarcoGasparian]]

==Question 18==

18. Alice takes one-third of the pennies from a large jar. Then Bret takes one-third of the remaining pennies from the jar. Finally, Carla takes one-third of the remaining pennies from the jar, leaving 40 pennies in the jar. How many pennies were in the jar at the start?

Step 1: The key concept to grasp in this particular question is that the 1/3 that Bret and Carla are taking are the REMAINDER of what had been left at the jar based on what had already been removed. Nevertheless, Alice, Bret, and Carla are all taking 1/3 of what is being offered to them.

Step 2: In order to figure out this problem you must think backwards, working from the solution. The question which I posed in my own mind was what equals 40 if its has 1/3 of it subtracted 3 times

Step 3: I looked at the number 40 and started testing different possibilities with numbers whose value of 1/3 was still an integer. I then realized that 60*1/3 = 20
60-20=40

20= The amount Carla took from the 60 Remainder from the 1/3 Alice took and then the 1/3 that Bret took (after Alice).

I repeated the process and realized that
90*1/3= 30
90-30= 60
30= Amount Bret took from the 90 remainder of the 1/3 Alice took.

I finally did the process a third time and realized that

135*1/3= 45
135-45=90
45= Amount Alice took from the TOTAL = 135
How many pennies were in the jar at the start? 135 pennies

Step 4: When I looked at the questions solution, I noticed that there was a pattern with the formula I was using.

Essentially the amount that remained was twice as much as the value a person had previously taken. This makes sense since we are subtracting 1/3 of the 3/3 leaving us with 2/3
(2/3)/(1/3)= 2 for every 1

[[User:MarcoGasparian|MarcoGasparian]]

==Question 23==
23. Suppose you overhear the following conversation: Paul: How old are your three children? Paula: The product of their ages is 36 and the sum of their ages is the same as today's date. Paul: That is not enough information. Paula: The oldest child also has red hair. If you were Paul could you determine the ages of Paula's children? Explain.

Step 1:In order to figure out this question I eliminated the useless information. The fact that the oldest child has red hair is a null point. I then formulated different possibilities in my head of what could be done if I were to try to solve this.

Step 2: I realized that the easiest way to figure out this problem is to create a factor tree of 36. 36 can be factored to 36*1, 2*18, 3*12, 4*9, 6*6, 4*3*3, 2*3*6, 2*2*3*3, 2*3*6 Note that the only possible answers were the ones that could be factored into 3 different numbers as there are exactly 3 children.

Step 3: The question also states that the sum was today’s date. Since today is the 12th, the only factor which would be possible is 2*3*6
Since the product of that equals 36 and the sum equals 12. Also, it could not have been 6*6 since it was asking for 3 children and not 2

Step 4: In order to check this I tried all different factors of 36 and saw through trial and error that this was the only compatible one.
[[User:MarcoGasparian|MarcoGasparian]]

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