6. Packaging By cutting away identical squares from each corner of a rectangular piece of cardboard and folding up the resulting Haps, an open box may be made. If the cardboard is 15 in. long and 8 in. wide, find the dimensions of the box that will yield the maximum volume.
7. Metal Fabrication If an open box is made from a tin sheet 8 in. square by cutting out identical squares from each corner and bending up the resulting flaps, determine the dimensions of the largest box that can be made.
8. Minimizing Packaging Costs If an open box has a square base and a volume of 108 in.’ and is constructed from a tin sheet, find the dimensions of the box, assuming that a minimum amount of material is used in its construction.
9. Minimizing Costs A pencil cup with a capacity of 36 in.3 is to be constructed in the shape of a rectangular box with a square base and an open top. If the material for the sides costs 15tf/in.2 and the material for the base costs 40e/in.2. what should the dimensions of the cup be to minimize the construction cost?