Optimization: Example 1
This classic problem is listed in practically every calculus textbook ever printed. Our goal is to find the maximum volume of a box possible – obtained by cutting four square corners out of a sheet of cardboard, and then folding up the sides. If the corners are too small the box will be wide but shallow, and have a low volume. If the sides are too tall and the base too small, the box will have a low volume. Somewhere in the middle is just right and we can find these optimal dimensions using Calculus.