We want to create a box with a square base made out of cardboard. The top will be double thickness and the bottom triple thickness. We want the box to hold 400 cubic inches and to use the least amount of cardboard.
a) Write an expression for C (the area of cardboard needed) in terms of s,the width of the base, and h, the height of the box.
b) Now write an expression for C in terms of just one of the variables (s or h).
This shows how to minimize cardboard needed to create a box with given volume.