An open rectangular box having a volume of 108 in.3 is to be constructed from a tin sheet. Find the dimensions of such a box if the amount of material used in its construction is to be minimal. Hint: Let the dimensions of the box be x x y x z. Then xyz = 108, and the amount of material used is given by S = xy + 2yz + 2xz. Show that the following is true and minimize f(x, y).