Consider the same open-top box, which is to have volume 216in³. Suppose the cost of the material for the base is $0.20/in² and the cost of the material for the sides is $0.30/in² and we are trying to minimize the cost of this box.

Write the cost as a function of the side lengths of the base. (Let x be the side length of the base and y be the height of the box.)