Question: (a) You have been asked to bid on the construction of a square-bottomed box with no top which will hold 100 cubic inches of water. If the bottom and sides are made from the same material, what are the dimensions of the box which uses the least material? (Assume that no material is wasted.)
(b) Suppose the box in part (a) uses different materials for the bottom and the sides. If the bottom material costs 5c per square inch and the side material costs 3c per square inch, what are the dimensions of the least expensive box which will hold 100 cubic inches of water?