Parameterized Optimization

Gave these two problems and made this to help with visualization. 1) A box is c times wider than it is long, and has volume V. Find the dimensions of the box that optimize the surface area. Will it be a minimum or a maximum? How do the parameters V and c affect the solution? Give a couple examples. 2) A box is c times wider than it is long and has surface area A. Can we find the box that optimizes volume? How do the parameters A and c affect the problem? Give a couple examples. Note: the aspect ratio adjusts to show the box, so pay attention to the axes.