Question

Can anyone help me set up an optimization problem? A box with a square base and open top must have a volume
of 32,000 cm . Find the dimensions of the box that minimize
the amount of material used.

Answer 1

So I know that b/c we have a square base, we're looking at x^2*height=32,000cm^3

Answer 2

I am stuck though, I can not set up the f(x) equation. My brain just isn't seeing it.

Answer 3

amount of material used. --- > total surface area = ... ?

Answer 4

I don't see what you're getting at?

Answer 5

so height * width * length = volume

Answer 6

thats correct, but you have to minimize amount of material used. --- > minimize total surface area

Answer 7

amount of material might be just h * w * 4, + w * l?

Answer 8

sure, I have to minimize my total surface area, yes

Answer 9

thats correct, with w=l

Answer 10

yes!, how do I set up my equation?

Answer 11

let x = width and length

Answer 12

32000=x^2 * l

Answer 13

I am NOT seeing this.

Answer 14

f(x) = 4 h x + x^2 [total surface area]
volume = 32000 = x^2 h
got this ?
h= height.

Answer 15

Height, that's right... still processing in my brain, though, sorry.

Answer 16

okay, I get the f(x), but am I tossing out my volume?