A container with square base, vertical sides, and open top is to be made from 2700 square feet of material. Find the dimensions (length × width × heigth) of the container with greatest volume.

Answer 1

volume=s^2*h s is the base length.

but 2700=s^2+4sh
from that, sh=(2700-s^2)/4

then
volume= s(2700-s^2)/4
now, take the derivative of with respect to s...

dV/ds=0=2700/4 -3s^2/4
solve for s

Answer 2

12X12x14