5. A box is made with a square bottom and an open top to hold a volume of 8 ft3. The width and height of the box are labeled as w and h, respectively, in the picture below. The material for the sides costs $5 per square foot and the material for the bottom costs $2 per square foot. Let C denote the cost of the box. We want to know what dimensions will minimize the cost of the box. (a) (3 points) Find a formula for C in terms of w and h. h W Answer: (b) (2 points) Write a constraint equation in terms of w and h that results from the fixed volume. Answer. (c) (2 points) Using (a) and (b) above, write C as a function of only w.(d) (5 points) Find the dimensions of the box (specifically w and h) that minimize cost C. You may leave your answers in exact form. Answer: (e) (2 points) Check you found a minimum for w in part (d) using a derivative test