Consider a box with length L, width W, and the height H. Assume you have to construct a box with the following constraint: W+L+H equal or less than 30.
1. Assume W has to be 12. Determine the maximizing volume of box? What should L and H be?
2. Assume the W has to be some number x element of set (0, 30). In order maximize volume of the box, what should L and H be?