A closed box with a square base is to have a volume of 252 3. The material to construct the box comes in different thicknesses. The bottom costs $0.05/2, the top costs $ 0.02/3, and the sides cost $ 0.04/2. Find the dimensions of the box that will minimize the cost [6] a) Determine the dimension of the box that will minimize the cost of the production. b) What is the minimum cost?