A box with a square base and open top must have a volume of 100 cm3 . The material for the bottom costs 5 cents per cm2 and the material for the sides costs 3 cents per cm2 . Find the dimensions of the box that minimize the cost of material used.

A fence is to be built to enclose a rectangular area of 300 square feet. The fence along three sides is to be made of material that costs 6 dollars per foot, and the material along the fourth side costs 12 dollars per foot. Find the length and width of the enclosure that is most economical to construct.