MATHEMATICS · Multi-part · CBSE · Mathematics · Applications of Derivatives · Applications of Derivatives
Problem
For a particular product, the total cost (in dollars) of producing q units is
C(q)=0.005q2+50q+10,000,q>0.
The firm wishes to operate at the production level that minimizes its average cost per unit.
(a) Define the average cost function AC(q) and simplify the expression.
(b) Determine the production level q that minimizes AC(q).
(c) Compute the minimum average cost, expressing your answer to the nearest cent.
(d) Explain, in economic terms, why producing either significantly fewer or significantly more than the quantity found in part (b) would increase the average cost.