A closed box with a square base is designed to have a surface area of 216 sq. ft. Find the dimensions of the box if the volume is to be a max.
Pardon my elementary approach to this.. but this is how I have been doing these sort of problems.. i make up 2 equations ...
6lw = 216 sq ft (surface area)
l^3 = maximum (volume of a cube, square on all sides)
then i solve for one of the variables, in this case L (length)
so 216/6w = 36/w = l
then i substitute
(36/w)^3 = maximum
do you guys follow? in this particular case, i get some weird numbers in the end, so i think my approach didn't work in this problem?