Let be the shipping cost (in dollars) for a package that weighs kilograms

MATHEMATICS · Subjective · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation

Problem

Let

C(w)

be the shipping cost (in dollars) for a package that weighs

w

kilograms, where

C(w)= \begin{cases} 8w+5, & 0\le w\le 20,\\ 6w+45, & 20< w\le 50. \end{cases}

The average cost per kilogram is

A(w)=\dfrac{C(w)}{w}

for

0<w\le 50

. Determine the weight

w

(in kilograms) that minimizes

A(w)

on this domain.