The top of a box is a rectangle with a perimeter of 72 inches. If the box is 8 inches high, what dimensions will give the maximum volume?

Answer 1

This question cannot be answered as it stands!

If the box is a rectangular parallelpiped (i.e. a box with all right angles), then

V = 8L(72-L) and dV/dL = 72*8 - 16L

and at the maximum L = 36, i.e. the top is a square as expected.