A rectangular box is to have a square base and a volume of 60 ft3. the material for the base costs 33¢/ft2, the material for the sides costs 10¢/ft2, and the material for the top costs 20¢/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.

The base and top have the same area, so we can add their costs.
.. cost of base + cost of top = (0.33 +0.20)*x^2 . . . . . . . . x measured in feet

The height of the box wil be (60/x^2), and the total length of all sides is the perimeter of the base, 4x. Then the cost of the sides is
.. cost of sides = (0.10)*(60/x^2)*(4x) = 24/x

The total cost of material for the box is
.. total cost = cost of base + cost of top + cost of sides
.. total cost = 0.53x^2 +24/x . . . . . . . . . . dollar cost for x in feet