A rectangular box is to have a square base and a volume of 30 ft3. The material for the base costs 33¢/ft2, the material for the sides costs 10¢/ft2, and the material for the top costs 24¢/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

Let each side of the base be x ft, and its height be h ft
Volume = x^2 h
30/x^2 = h

cost of base = 33x^2
cost of sides = 10(4)(xh) = 40x(30/x^2 = 1200/x
cost of top = 24x^2

cost = 57x^2 + 1200/x