Part C: For the following word problem, you need to show all of your work. Explain what you are doing at each step and why you are doing the steps. When you come to a final answer, verify by using what we have done in chapter 4 that shows you truly have a minimum or maximum. (I would like your work/answers to be such that anyone could pick up this problem and understand why you are doing what you are doing. Write clearly.)

Your company has contracted to design and build a 108 ft3, square-based, open-top, rectangular steel holding box for a paper company. The box is to be made by welding stainless steel plates together along their edges. As the production engineer, your job is to find the dimensions for the base and height that will use the least amount of steel. What dimensions do you tell your company to use? (Hint: you will want to minimize surface area.)