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  

step-by-step explanation:

12: 00 p.m. to 7: 00 p.m. is a total of 7 hours.

4: 00 p.m. to 7: 00 p.m. is a total of 3 hours.

this means that from 4: 00 p.m to 7: 00 p.m. this represents 3/7 of what was lost from 12: 00 p.m. to 7: 00 p.m.

after knowing this, after doing 11,600 - 6,800 = 4,800

4,800 represents 3/7 of what was lost for 7 hours.

we then divide 4,800 by 3 which gets 1,600.

because we know that 1,600 represents 1/7 of how much water was lost, we just have to multiply by 7, which gets 11,200.   after adding 11,200 to how much water was left at 7: 00 p.m. which was 6,800. 11,200 + 6,800 = 18,000

this means that the pool originally had 18,000 gallons in the pool.

you can also check your work by doing 18,000 - 4(1600), which becomes           1800 - 6400 which gets you 11,600.