(20 points total) A manager must decide on the mix of products to produce for the coming week. Product A requires three minutes per unit for molding, two minutes per unit for painting, and one minute per unit for packing. Product B requires two minutes per unit for molding, four minutes per unit for painting, and three minutes per unit for packing. There will be 600 minutes available for molding, 600 minutes for painting, and 420 minutes for packing. Both products have profits of $1.50 per unit. a. (10 points) Formulate the above problem as a linear program in order to maximize profit. () Define the variables, (i) formulate the objective function, and (in) all constraints. Don't solve! b. (4 points) The optimal solution is to produce 150 units of Product A and 75 units of Product B. Determine the objective function value at optimality. C. (6 points) Are any of the three resources - molding, painting, and packing time left unused at optimality? If so, how much