By cutting away identical squares from each corner of a rectangular piece of cardboard and folding up the resulting flaps, an open box is made. If the cardboard is 15 in. long and 8 in. wide and the square cutaways have dimension of x in. by x in., find a function for the volume as a function of x of the resulting box(See picture in the text.)

A rectangular box is to have a square base and a volume of 20 ft3. The material for the base costs 30 cents/ft2, the material for the sides costs 10 cents/ft2, and the material for the top costs 20 cents/ft2. Letting x denote the length of one side of the base, find the function x giving the cost of constructing the box.