Simple Optimization Problem?

[Assassin315]

This doesn't sound too hard, but I'm having issues when it comes to starting in the right place.

You've basically trying to make a box with a lid from a square sheet of material, 18 inches on each side. Picture attached. Sorry in advance. The red shapes are the specified cuts.

Anyways. I want to make sure how to start this without any indication of what the lengths are. I know the two sides are going to be "18 - 2(square length)" and "18 - 2(rectangle + square length), but how do I set it up so that I can later use calculus to optimize it?

 

[galactus]

If you cut squares out of one end and rectangles out of the other, when you fold up the sides it is going to look rather lop-sided.

It will not make a very good box because one side will stick up higher than the other side. For a box, the cut out portions should be the same size.

If squares are cut out, then the volume would be \(\displaystyle V=x(18-2x)(18-2x)\)