The United States Post Office will not accept a box whose girth (distance around) plus length is more than 108 inches. Suppose that we want to build a container with a square base whose volume is as large as possible and whose girth plus length is precisely the maximum 108 inches. Model this situation by letting x be the length of the side of the square base, and expressing the volume in terms of x. Then use your calculator to estimate the dimensions of the box.

Find a rectangular piece of paper, cardboard, poster-board, etc. to create a box. Measure the sides of your paper and record them below (if you are using a normal size piece of paper its dimensions are 8.5 inches by 11 inches). You will now have to determine the length, width, and height to make an open-top box with the maximum volume possible. To do this you will have to cut the corners of the paper to fold up (but don't do this yet). Assume the height of the box will be x, which means you will need to subtract x from both sides of the width and length. Use these three dimensions to create a volume equation which you can derive like we did yesterday to find the optimal value for x leading to the maximum dimensions for your box. All of your work and the box you create should be submitted below.