U-Pack-Em sells cardboard boxes for the do-it-yourself mover. Their most popular size has a volume of 2
cubic feet. As shown in the figure below, the top and bottom are made using four flaps. The price of
cardboard is $0.20/ft'. What are the raw materials cost and dimensions for the cheapest box that can be
manufactured? (Be sure to show that it is, in fact a minimum by looking at the Hessian Matrix.)
The solution gives detailed steps on finding minimum area and cost for a box. We use Hessian matrix to check the validity of minimum. Attached as Word.