1. ## Questions about Optimization Problems

1. An open box is to be made from a 3x4 piece of paper by cutting equal squares from each corner. Find the volume of the largest box.

Question: Okay, this is ridiculous, but if my x-value turns out (7+/-√31) / 6, how do I know which value to use?

2. A paper contains 45 square inches of print. The margins at top/bottom are 1.5 in. At each side, they are 1 in. What are the dimensions in order to have a minimum amount of paper?

The answer's √30 x (3√30)/2, but I'm not getting the same answer.

3. Find the point on the graph of y=x^3 closest to the point (2,0).

Question: Do I just use the distance formula for this?

Any help is greatly appreciated.

Thanks!

how do I know which value to use?
Domain!!

It makes no sense to cut out a square with NEGATIVE sides, so x > 0.

If you have a 3" side, you cannot cut squares more that 1.5" (Why?), so 0" < x < 1.5".

Which, if any, of your possible solutions is in that Domain?

3. Wow, I feel like an idiot.

Haha, thank you for your help!