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9-39.
  1. 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 ✎

    1. Write an expression for the cost of the base in terms of x.

    2. Express the cost of the sides in terms of x and h, the height of the box.

    3. Express the total cost of the box in terms of x and h.

    4. 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.

    5. 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: x2
Cost: 3x2

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

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

100 = x2h

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