### Home > PC3 > Chapter 4 > Lesson 4.1.1 > Problem 4-13

The manufacturing company you work for has been hired to produce a

Sketch a diagram of this situation.

Sketch a box and label the sides of the base

and the height.Write an expression for the cost of the base in terms of

.base cost

(area of the base) Express the cost of the sides in terms of

and, the height of the box.side cost

(length of base)(height)

How many sides does the box have?Express the total cost of the box in terms of

and.total cost

base cost cost of all sides Use the fact that the volume of the box is

cubic feet to write an equation for the volume of the box. (area of the base)(height)(area of the base)(height) Solve for

*h*in your equation from part (e) and then express the cost only in terms of.Graph your equation from part (f) to determine value of

that gives the minimum cost. What is the minimum cost?