Question

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

Answer 1

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