A builder wishes to construct a warehouse with a square front and a volume of 500 cubic meters. Find a formula in terms of x for the total construction cost C(x) of the warehouse.

Let x be the side of the square front.

x^2 is the area of the square front.

Let l be the length of the base, then xy is the area of the base.

The total area of the warehouse, for 4 walls and a roof is thus: 2x^2 + 3xy

The volume of the warehouse is given by 500 = x^2y

The construction, I assume, is based on the area (amount of concrete or other materials needed). Use the second equation with volume to get the area in terms of x only.