The Presented Problem

The problem presented is a volume problem. You are given the length (11 inches) and width (8.5 inches) of a letter size piece of paper. You are told to cut out four corners of the piece of paper and fold the “flaps” to make a box without a top.

The diagram is shown below:

For the first part, you are asked to find the dimensions that will give you the largest box.

For the second part, you are asked to find the dimensions of the largest box using a length of 14 inches and keeping the same width.

Finally, you are asked to generalize for a rectangular piece of paper of any dimension.

Next, I begin working though part one.