a box with a square base and open top must have a volume of 32000 cm^3. find the dimensions of the box that minimize the amount of material used

Question

a box with a square base and open top must have a volume of 32000 cm^3. find  the dimensions of the box that minimize the amount of material used

fibonaccichick666 · Answer

fyi I like your name.  2 how shall we approach this? any ideas?

anonymous · Answer

This is a basic optimization problem using calculus. The volume = l*w*h The surface area is what we're trying to minimize, and it equals h*w*2+h*l*2 + l*w (taking l*w=the bottom, the top does not exist)

anonymous · Answer

thanks. I'm trying to figure out how to go about it but I'm struggling with where to begin.

anonymous · Answer

There are your two functions. Oops! Square base... OK, that simplifies things.$$ Volume =x ^{2} y$$ where x is the side length on the base and$$ area= x ^{2} + 4 xy$$ Set volume equal to 32000, solve for x, replace y with x in your equation, and minimize.

anonymous · Answer

Nice.  Thanks for the info.  I'll give it a shot and I'll report back with my findings.