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

The manufacturing company you work for has been hired to produce a 100 cubic foot box. It must have a square base and no top. The material for the base costs $3 per square foot and the material for the sides costs $1 per square foot. We want to write an equation for the cost of the box as a function of

*x*, the length of one edge of the base. Homework Help ✎Write an expression for the cost of the base in terms of

*x*.Express the cost of the sides in terms of

*x*and*h*, the height of the box.Express the total cost of the box in terms of

*x*and*h*.Use the fact that the volume of the box is 100 cubic feet to eliminate h from the equation you just wrote and express the cost solely in terms of

*x*.Graph the equation and find the value of

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

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

Area: *x*^{2}

Cost: 3*x*^{2}

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: 4*xh*

Cost: (1)(4*xh*) = 4*xh*

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

100 = *x*^{2}*h*

Substitute '*h*' into the equation in part (c).