In: Math
A peanut can has the usual “can shape” of a circular cylinder. Its sides are made of cardboard, its bottom is made of thick plastic-coated aluminum foil, and its top lid is made of clear plastic. It must have a volume of 480 cubic centimeters. The cardboard material used for the sides costs 0.1 cents per square centimeter, the foil material used for the bottom costs 0.3 cents per square centimeter, and the plastic material used for the top lid costs 0.5 cents per square centimeter. What dimensions should the can have in order to minimize the cost of the materials from which it is made?