Two numbers have a difference of 14. Determine the two numbers and their product if their product is a minimum.

Warren and Joe have fifty dollars between them. How should they divide the money to that the product of the amounts is a maximum?

I know how to find it just by thinking, because it is common sense, however how would I prove it by using quadratics?

Sarah, Please stop posting YOUR homework in this manner.
If you would like HELP, then fair enough, but please show us that YOU have at least attempted to answer these questions on your own.