A manufacturer’s total cost (in dollars) for producing units is modeled by…

MATHEMATICS · Single correct · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation

Problem

A manufacturer’s total cost (in dollars) for producing

q

units is modeled by

C(q)=0.005q^{3}-0.3q^{2}+10q+200, \quad 0\le q\le100.

For which production level

q

does the average cost

\dfrac{C(q)}{q}

attain its absolute minimum on this interval? (a)

q=30

(b)

q=100

(c)

q\approx42

(d)

q=50