5. Suppose you wish to construct a rectangular box with a volume of 32 cubic feet. Three different materials will be used in the construction. The material for the sides costs $1 per square foot, the material for the bottom costs $3 per square foot, and the material for the top costs $5 per square foot. What are the dimensions of the least expensive such box? 6. Find the local maxima and minima of (, ) = 3 3 + 9y