Given the cost function C(q) = 4000 + 50q + 0.002q2 and the demand function p = 80 - 0.025q, find the value of q for which:
(a) Average cost is a minimum.
(b) Revenue is a maximum.
(c) Profit is a maximum.
Quadratic equations are manipulated to figure maximum and minimum values for average cost, revenue and profit. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.