Problem 7-11 (Algorithmic) Hart Manufacturing makes three products. Each product requires manufacturing operations in three departments: A, B, and C. The labor-hour requirements, by department, are as follows: | | Department B L Product 1 | Product 2 1.60 3.10 2.20 1.20 0.35 0.35 Product 3 2.10 2.70 0.35 | During the next production period, the labor-hours available are 470 in department A, 370 in department B, and 70 in department C. The profit contributions per unit are $27 for product 1, $30 for product 2, and $32 for product 3. Use a software package LINGO. a. Formulate a linear programming model for maximizing total profit contribution. For those boxes in which you must enter subtractive or negative numbers use a minus sign. (Example: -300) If constant is "1", it must be entered in the box. Let P; = units of product i produced Max 27 P. + C30 PO 32 P3|| s.t. 1.60 2.20 0.35 Pal+ Pal+ P11+ 3.10 P2 + 1.20 P2 + 0.35 P2 + P1, P2, P320 2.10 2.70 0.35 P3 P3 Pals 470 370 70 b. Solve the linear program formulated in part (a). How much of each product should be produced, and what is the projected total profit contribution? b. Solve the linear program formulated in part (a). How much of each product should be produced, and what is the projected total profit contribution? P1 = Profit = $ C. After evaluating the solution obtained in part (b), one of the production supervisors noted that production setup costs had not been taken into account. She noted that setup costs are $420 for product 1, $570 for product 2, and $620 for product 3. If the solution developed in part (b) is to be used, what is the total profit contribution after taking into account the setup costs? Profit = $ d. Management realized that the optimal product mix, taking setup costs into account, might be different from the one recommended in part (b). Formulate a mixed-integer linear program that takes setup costs into account. Management also stated that we should not consider making more than 185 units of product 1, 160 units of product 2, or 150 units of product 3. For those boxes in which you must enter subtractive or negative numbers use a minus sign. (Example: -300) If the coefficient of a constraint is "1", enter "1" in the answer box. Enter "o" if a coefficient or a RHS value is zero. Here introduce a 0-1 variable ythat is one if any quantity of product iis produced and zero otherwise. d. Management realized that the optimal product mix, taking setup costs into account, might be different from the one recommended in part (b). Formulate a mixed-integer linear program that takes setup costs into account. Management also stated that we should not consider making more than 185 units of product 1, 160 units of product 2, or 150 units of product 3. For those boxes in which you must enter subtractive or negative numbers use a minus sign. (Example: -300) If the coefficient of a constraint is "1", enter "1" in the answer box. Enter "o" if a coefficient or a RHS value is zero. Here introduce a 0-1 variable yi that is one if any quantity of product i is produced and zero otherwise. Max P1 P2 P319 yal + TT + + VI + + VIL WSDL + + VI + VI VI VI e. Solve the mixed-integer linear program formulated in part (d). How much of each product should be produced, and what is the projected total profit contribution? Compare this profit contribution to that obtained in part (c). Enter "o" if your answer is zero. Profit = $ The profit is by $