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 Product 1 Product 2 Product 3 A 1.50 3.00 2.00 B 2.00 1.00 2.50 C 0.25 0.25 0.25 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 145 units of product 1, 155 units of product 2, or 195 units of product 3. (Let P; = units of product i produced and y; be the 0-1 variable that is one if any quantity of product i is produced and zero otherwise, for i = 1, 2, 3.) What is the objective function of the mixed-integer linear program? Max In addition to the constraints from part (a), what other constraints should be added to the mixed-integer linear program? s.t. units of Product 1 produced units of Product 2 produced units of Product 3 produced P1, P2 P2, P3 = 0; Y1, 12, 13 = 0, 1 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 (in dollars) contribution? (P1, P2, P3, V1, Y2, Y 3) = with profit $ 4330 X. 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 Product 1 Product 2 Product 3 A 1.50 3.00 2.00 B 2.00 1.00 2.50 C 0.25 0.25 0.25 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 145 units of product 1, 155 units of product 2, or 195 units of product 3. (Let P; = units of product i produced and y; be the 0-1 variable that is one if any quantity of product i is produced and zero otherwise, for i = 1, 2, 3.) What is the objective function of the mixed-integer linear program? Max In addition to the constraints from part (a), what other constraints should be added to the mixed-integer linear program? s.t. units of Product 1 produced units of Product 2 produced units of Product 3 produced P1, P2 P2, P3 = 0; Y1, 12, 13 = 0, 1 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 (in dollars) contribution? (P1, P2, P3, V1, Y2, Y 3) = with profit $ 4330 X
