12. Find the dimensions of the rectangle of maximum area, with sides parallel to the coordinate axes, that can be inscribed in the ellipse with equation -+ 1. 100 16 13. Find the point on the line y = -2x + 3 that is closest to the point (-2, 1). 14. Find the point on the parabola y = (x - 3)2 that is closest to the origin. 15. A rancher has 400 ft of fencing with which to enclose two adjacent identical rectangular parts of a corral. What are the dimensions of the parts if the area enclosed is to be as large as possible and she uses all of the fencing available? 16. An open box constructed from a tin sheet has a square base and a volume of 216 in. Find the dimensions of the box, assuming that the minimum amount of material was used in its construction. 17. A closed rectangular box with a volume of 4 fts is to be constructed. The length of the base of the box will be twice as long as its width. The material for the top and bottom of the box costs 30 cents per square foot, and the material for the sides of the box costs 20 cents per square foot. Find the dimensions of the least expensive box that can be constructed