plaill. 14. A box with a square base and no top must have a volume of 10 000 cm3. If the smallest dimension is 5 cm, determine the dimensions of the box that minimize the amount of material used. 15. An animal breeder wishes to create five adjacent rectangular pens, each with an area of 2400 m2. To ensure that the pens are large enough for grazing, the minimum for either dimension must be 10 m. Find the dimensions required for the pens to keep the amount of fencing used to a minimum. 16. You are given a piece of sheet metal that is twice as long as it is wide and has an area of 800 m . Find the dimensions of the rectangular box that would contain a maximum volume if it were constructed from this piece of metal by cutting out squares of equal area at all four corners and folding up the sides. The box will not have a lid. Give your answer correct to one decimal place. 17. A cylindrical can needs to hold 500 cm3 of apple juice. The height of the can must be between 6 cm and 15 cm, inclusive. How should the can be constructed so that a minimum amount of material will be used in the construction? (Assume that there will be no waste.)