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

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.

MODEL: C(n) = 7(n-20)+100

N = number of items C =the cost

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

Our model predicts that for the production of 150 items it will cost $1010.

C(150)= 7(150-20)+100 C(150)= 1010

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

According to our model C(n) = 7(n-20)+100

As production continues:

C(150)= 7(150-20)+100 = 1010

C(200)= 7(200-20)+100 = 1360

C(250)= 7(250-20)+100 = 1710

C(300)= 7(300-20)+100 = 2060

Average cost is: Total Cost / # of Units made.

AC(150)= 1010/150 = 6.7333

AC(200)= 1360/200 = 6.8

AC(250)= 1710/250 = 6.84

AC(300)= 2060/300 = 6.8666

The Average Cost per Unit made will increase as production continues.

Other models which you get different behaviours are as followed:

The average cost remains constant as production increases:

C(x)= x * n

X = Marginal Cost $5 N = # of Units produced

As Production Continues:

C(150)= (5)(150)= 750

C(200)= (5)(200)= 1000

C(250)= (5)(250)= 1250

C(300)= (5)(300)= 1500

Average Cost:

AC(150)= 750/150= 5

AC(200)= 1000/200= 5

AC(250)= 1250/250= 5

AC(300)= 1500/300= 5

The Average Cost per Unit produced is held constant.

The average cost decreases as production increases:

The slope increases but at a slower and slower rate as production increases which represents a decrease in average cost.

The average cost increases as production increases.

The slope represents the cost per unit in this model the slope increases at a faster and faster rate as production continues. This represents increase average cost.

You obtain an economy of scale.

We can see in this diagram that with the economy of scale there is a reduction in cost per unit resulting from increased production and operational efficiencies. Economics of scale shows that increase production causes the cost of each additional unit to fall.