Chapter 6.3, Problem 19E

In Exercises 15-22, assume that relative maximum and minimum values are absolute maximum and minimum values.

Minimizing the cost of a container. ProHauling Services is designing an open-top, rectangular container that will have a volume of 320 ${\text{ft}}^3$. The cost of making the bottom of the container is $5 per square foot, and the cost of the sides is $4 per square foot. Find the dimensions of the container that will minimize total cost.

(Hint: Make a substitution using the formula for volume.)