# Thread: Optimization Word Problems

1. A topless square box is made by cutting little squares out of the four corners of a square sheet of metal 12 inches on a side, and then folding up the resulting flaps. What is the largest side area which can be made in this way?

What information I have so far is that since the side of the little squares are unknown, I called them "x", and so since the length of the full box is 12 inches, once folded up I'd have 12-2x. One thing I'm having trouble with is setting up my equation. I've done a similar problem before where it asks for volume, but I dont fully understand what it means by "side area." I also need to complete the perfect square to find dimension of the cut-out squares that result in largest possible side area.

2.

3. four sides, each with area $x(12-2x)$

therefore, total side area, $A = 4x(12-2x)$

4. I would be inclined to think that "side area" means "area of the sides" which is what what skeeter calculated.

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