Box Function Word Problem

Question

A rectangular box is to have a square base and a volume of 40 ft3. The material for the base costs 42¢/ft2, the material for the sides costs 10¢/ft2, and the material for the top costs 27¢/ft2. Letting x denote the length of one side of the base, find a function in the variable x giving the cost (in dollars) of constructing the box.

Answer 1

x represents the length of one side of the base

40/x² represents the height of the box

 

The cost of the base is 42x²

The cost of the top is  27x²

The cost of each side is 10(x)(40/x²), or 400x

The cost of the four sides is 1600x

 

Cost = 42x² + 27x² + 1600x

Cost = 69x² + 1600x