Of all boxes with a square base and a volume of 100m , which one has the minimum surface area? (Give its dimensions)

Question

Of all boxes with a square base and a volume of 100m  , which one has the minimum surface area? (Give its dimensions)

anonymous · Answer

hey am sorry jkp, in maths we always not have a volume with that unit (100m) .what is it

anonymous · Answer

So I started out with the following equations:

constraint: $$w ^{2}h = 100 $$
objective: $$S = 2w ^{2}+4hw$$
Then I proceeded to solve for h using the first equation, and substituted that 
expression into the second equation. Next I took the derivative and sett it equal
to zero to find the critical points and got w = -100, but that is where I got stuck.
How do I use that to find the dimensions?|dw:1340461277562:dw|