I worked out this problem today, and thought it was quite neat, so I posted it for anyone else to try:

An open-topped box, has dimensions a, b, (base) and c (height). If the surface area of the box is 100m<sup>2</sup> (outside only), find the largest volume of the box. The faces of the box are 2D (0 thickness).

It probably won't be a hard question for some of you but I thought it was quite a nice little application of what I'm learning.