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 in. by y in. by z in. 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). a) s = f(x, y) = xy + 216/x + 216/y
b) x= ? in.
c) y= ? in.
d) z= ? in.