You want to build a box for your cat to sleep in. The box must have a square top, a square bottom, and 33 sides. The plush material for the square bottom costs $44 per square foot, the material for the sides costs $22 per square foot, and the material for the top costs $0.50.5 per square foot. You need a box with volume 1212 feet cubed. What are the dimensions of the box that minimize the cost? What is that minimum cost? Show all your work.