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

team valais homework 11

1) The model that we are going to use in this part is:

C(x)= 100 + 7(x-20), x>20

The above models is a linear equation. At first we are told that we have to spend 100$ (fixed cost) for the production of the first 20 units. Later on we are told that for any extra unit we have to pay 7$ (Variable cost). The variable 'x' in the above equation indicates the amount of units bought minus the initial 20 units that have to be subtracted because they are worth 100$. Or to describe it short: (x-20) is for the number of units to be multiplied by 7 to get the addition cost of producing 1 more unit.

2) Using the above equation our model predicts the following value for 150 units: C(150) = 100 + 7(150-20)= 1010

What we can conclude from the above equation is that for 150 units we will have a Total cost of 1010$.

3) Now in order to find the Average Cost of per item produced we have to do some modification to the model introduced in no.1. Average Cost (A(x)) is the derivative of C(x).

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

A(x) = 40x^(-2)

The average cost per item increases as production levels increase.

Other models (not necessarily linear) for which you get other behaviors such as:

1. The average cost remains constant as production increases. A(x) = 5 C(x) = 5x

2. The average cost diminishes as production increases. A(x) = 1/x^2 C(x) = 1/x

3. The average cost increases as production increases. A(x) = x C(x) = x^2

4.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.

A(x) = (x-10)^2 + 10 C(x) = x(x-10)^2 + 100 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.