What will the dimensions of the resulting cardboard box be if the company wants to maximize the volume and they start with a flat piece of square cardboard 20 feet per side, and then cut smaller squares out of each corner and fold up the sides to create the box?
Suppose that the squares removed from each corner are
When these are folded up they give a box with a height of
and a base of
for a volume
To find the critical point(s) take the derivative of
The resulting box will be