Course:MATH110/Archive/2010-2011/003/Teams/Vaud/Homework 11
Homework 11
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.
What does your model predict for a production of 150 items? According to your model, what happens to the average cost per item as production levels increase?
From the above information we can see that it costs $7 per flag and $5 per flag for quantities of flags greater than 20 (we know this because $100/20 flags = $5). Since there is a price difference for different quantities of flags, we can create two models to show the cost.
Model 1: Cost to produce less than 20 Vaud flags
C= total cost of flags
V= number of Vaud flags produced
For example: How much will it cost to produce 15 Vaud flags?
Model 2: Cost to produce more than 20 Vaud flags
We can see from the above information that it costs $100 to create 20 Vaud flags. However, if we had used model 1 to find out the cost, we would see that it costs $140. This is a difference of $40. With this difference in mind, we can now write the model as:
For example: I want to produce 20 flags. How much will this cost me?
How much will it cost to produce 150 flags?
C(150)=1010
This model can also be derived from its graph. If we denote the x-axis to be the number of flags produced and the y-axis to be the cost we can take a point from the graph (20,100) and use this point to find the equation of the line. The point (20,100) was chosen because it costs $100 to make 20 Vaud flags. As stated above, the marginal cost is $7 and this is known to be the slope of the line.
100= 7(20)+b
100=140+b
b=-40
y=7x-40 (the same equation as model 2)