MATHEMATICS · Multi-part · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation
Problem
For a certain small manufacturing plant, the total daily cost of producing q units is modeled by
C(q)=0.1q3−6q2+150q+5000,0<q≤100,
where C(q) is measured in dollars.
(a) Define the average cost function A(q) and compute A′(q).
(b) Determine the production level that minimizes average cost on the given interval, and verify that your result yields a minimum.
(c) Calculate the minimum average cost and the corresponding total cost at the production level found in part (b).
(d) Compare the marginal cost C′(q) to the average cost A(q) at the production level that minimizes average cost, and explain the economic significance of your observation.