# Thread: Optimization Problems (Quick Question)

1. ## Optimization Problems (Quick Question)

I'm on my way to solving this problem, I just need a little help.

"The volume of a square-based rectangular cardboard box is to be 1000cm^3. Find the dimensions so that the quantity of material used to manufacture all 6 faces is a minimum. Assume that there will be no waste material. The machinery available cannot fabricate material smaller in length than 2cm."

Knowing that it is a square-based shape, you can assume that length = width = height. Therefore, V = x^3. Easy.

The volume of the cardboard box has to be 1000cm^3.

Therefore, 1000cm^3 = x^3. The domain in this problem is 2 < x < ____.

I don't know where to go from here, could someone provide some insight?

How do I figure out the maximum end point for the domain, and what would my next step be?

2. careful, I don't think this problem is talking about a cube, I think it's talking about a square prism. In that case only two of the dimension must be equal, so you'll be dealing with $V=x^2y$, and $S=2x^2+4xy$ where S is the surface area that you are trying to minimize. Rewrite S in terms of x (using the V equation) and you'll have a clearer picture of the bounds of x.

3. Thanks, I solved it with your help.