### Home > AC > Chapter 16 > Lesson 16.9.1.3 > Problem 9-39

The manufacturing company you work for has been hired to produce a , the length of one edge of the base.

Write an expression for the cost of the base in terms of

.Write and expression for the area and multiply that by the cost per square foot.

Area:

Cost:Express the cost of the sides in terms of

and, the height of the box.Write an expression for the area of one side.

Write an expression for the area of four sides.

Write an expression for the cost of four sides.Area:

Cost:Express the total cost of the box in terms of

and.This is the sum of your expressions from parts (a) and (b).

Use the fact that the volume of the box is

cubic feet to eliminate h from the equation you just wrote and express the cost solely in terms of .Substitute '

*h*' into the equation in part (c).Graph the equation and find the value of

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