The average cost of producing 100 units is how much?

Question

A manufacturer has determined the marginal-cost function dc/dq below, where q is the number of units produced. If marginal cost is $90.00 when q=50 and fixed costs are $7000what is the average cost of producing 100 units?
 dc/dq=.012q2−0.6q+90
The average cost of producing 100 units is how much?

Answer 1

dc/dq = 0.012q² - 0.6q + 90

 

C(0) = fixed cost = $7000

 

C(q) = ∫[0.012q² - 0.6q +90]dq

 

        = 0.004q³ - 0.3q² + 90q + K

 

Since C(0) = 7000, we have K = 7000

 

So, C(q) = 0.004q³ - 0.3q² + 90q + 7000

 

Average cost = C(q)/q

 

When q = 100, Average cost = C(100)/100 = $170 / unit