I need help with two optimization problems. The first one involves the volume of a box and I have no idea what the second problem is asking.
1) If 1200 cm^2 of material is available to make a box with a square base and an open top, find the largest possible volume of the box?
2) (a) Show that of all the rectangles with a given area, the one with smallest perimeter is a square.
(b) Show that of all rectangles with a given perimeter, that one with greatest area is a square.