Find the dimensions of an open topped box that can be made from 3600 cm^2 of cardboard, if the length of the base is three times as long as its width. What is the maximum volume?

Answer 1

a = 3w^2 + 2(wh + 3wh) = 3w^2+8wh
since a=3600,

h = (3600-3w^2)/8w

The volume is 3w^2h = 3w/8 (3600-3w^2)

find the derivative, set it to zero, and you will find that w=20.

So, h=15 and the maximum volume is 20x60x15 = 18000