Amira manufactures jeans and has determined the marginal cost function. where q is the number of pair jeans produced. If marginal cost is 55.00$ when q=50 and fixed costs are 2000$. what is the average cost of the producing 200 pairs of jeans?.

dc/dq=0.006q^2-0.6q+70

Given

c' (q) = dc/dq=0.006q^2-0.6q+70

Integrate marginal cost to get cost function

c (q) = 0.002q^3-0.3q^2+70q+C (C is a constant)

Fixed cost = 2000 means that C=2000.

or

c (q) = 0.002q^3-0.3q^2+70q+2000

Average cost=c (q) / q, for q=200,

= (0.002*q^3-0.3*q^2+70*q+2000) / q

=20000/200

=100

Answer: Average cost is $100