# Optimazation math homework

1. Oct 28, 2004

### jenjen07

I'm lost with this problem. If anyone can help at all I'd really appreciate it.

What are the dimensions of the base of the rectangular box of greatest volume that can be constucted from 100 suqare inches of cardboard if the base is to be twice as long as it is wide? Assume that the box has a top.

I tried it and I got my voume to equal 100x^2-4x^4 divided by 3x. Maybe I have the equation wrong. Thanks for your help.

Jen

2. Oct 28, 2004

### StatusX

the sides of the bottom of the box are x and 2x, and the height is y, so you want to maximize the volume:

$$V= 2x^2 y$$

with the constraint that the surface area is 100:

$$4x^2 + 2x y + 4 x y = 100$$

You could solve for y in the constraint equation, plug that in for the volume and maximize, or you could use a lagrange multiplier.