Course:MATH110/Archive/2010-2011/003/Teams/Neuchatel/hw1

Homework #11

Our Model

In order to predict the cost of producing flags of Team Neuchatel, we created the model

C(f) = 7(f - 20) + 100

We got this formula by separating two different assumptions made. The first one being that the first 20 items produced had an overall cost of $100. When producting level exceeds 20, the marginal cost for one additional item would be $7. This is why we > have (x - 20) multiplied by 7, which is the cost of the additional items. And we add $100 to represent the cost of the first 20 items that we subtracted in the first part of the function.

Our predicts a cost of $1010 for a production of 150 flags.

C(150) = 7(150 - 20) + 100

C(150) = 7(130) + 100

C(150) = 910 +100

C(150) = 1010

The average cost per item is defined by total cost divided by quantity. With our model, as the production level increases, the average cost increases as well.

Production level of 150 flags

C(150) = 1010

AC = 1010/150

AC = 6.73

Production level of 160 flags

C(160) = 1080

AC = 1080/160

AC = 6.75

Production level of 170 flags

C(170) = 1150

AC = 1150/170

AC = 6.76

Production level of 180 flags

C(180) = 1220

AC = 1220/180

AC = 6.77

Another observation of the change in average cost as production level increases is that the difference between them becomes smaller.

Other Models

Average cost remains constant as production increases

In order for average cost to remain constant as production increases, marginal cost must also stay constant.

The model that we came up with is:

C(f) = MC * number of flags

If the Marginal Cost (MC) is $5, then

C(f) = 5f

If 10 flags are produced then the cost would be:

C(10) = 5(10)

C(10) = 50

And the average cost would be:

AC = TC/Q

AC = 50/10

AC = 5

If 20 flags are produced then the cost would be:

C(20) = 5(20)

C(20) = 100

And the average cost would be:

AC = TC/Q

AC = 100/20

AC = 5

If 30 flags are produced then the cost would be:

C(30) = 5(30)

C(30) = 150

And the average cost would be:

AC = TC/Q

AC = 150/30

AC = 5

Average cost diminishes as production increases

In order for average cost to decrease as production increases, marginal cost must be less than the average cost.

Average cost increases as production increases

In order for average cost to increase as production increases, marginal cost must be higher than average cost.