The weekly marginal cost of producing x pairs of tennis shoes is given by the following function, where C(x) is cost in dollars.

C'(x)= 16+ (200/(x-1))

If the fixed costs are $2,000 per week, find the cost function. C(x)=??

What is the average cost per pair of shoes if 1,000 pairs of shoes are produced each week?

The cost function is .

The average cost of 1000 shoes is $19.38.

Step-by-step explanation:

We define the marginal cost function to be the derivative of the cost function or .

To find the cost function, we need to integrate the marginal cost function

We know that the fixed costs are $2,000 per week, so the constant is equal to 2000, and the cost function is

If is the cost function for some item then the average cost function is,

We know that 1,000 pairs of shoes are produced each week, so the the average cost is  

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step-by-step explanation:

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step-by-step explanation

2r= 2300

r =1150