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: Product 1 3.00 1.00 0.25 Product 2 2.00 2.50 0.25 Product 3 1.50 2.00 0.25 During the next production period the labor-hours available are 450 in department A, 350 in department B, and 50 in department C. The profit contributions per unit are $28 for product 1, $30 for product 2, and $25 for product 3. (a) Formulate a linear programming model for maximizing total profit contribution. If the constant is "1" it must be entered in the box. If required, round your answers to two decimal places. Let P-units of product i produced Max $ s.t. P2 + P3 P2Select your answer P1+ P2+ P3Select your answer - v Select your answer- P1+ Pa + P1, P2P320 (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? Product 1 Product 2 Product 3 Amount to Produce Profit () After evaluating the sclution abtained in part(b,one of the production supervisors nated that production setup costs had not been taken into accounit. She noted that setup costs are $600 far product 1, $550 for praduct 2, and $400 for product 3. If the solution daveloped in part (b) is to be used, what is the total profit contribution after taking into account the setup costs? (d) Management realized that the optimal product mix, taking setup costs into account, might be different frorm the one recommended in part (b).Farmulate a mixed integer linear pragram that takes setup costs pravided in part (c) into account. Management also stated that we should not consider making more than 175 units of praduct 1, 150 units af product 2, ar 140 units of product 3. What are the new objective functian and additianal equation constraints? If the constant is "1 it must be entered in the box Let Y is one if any quantity af product i is praduced and zero otherwise. Max Pi+ th! Y2 s.t Gselect your answer . -]Ya P1 PzSelect your answer Select your answer P:, P2, P 2 0 (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). If required, round your answers to nearest whole number. If your answer is zero enter Product 1 Product 2 Product 3 Amount to Produce Updated Profit 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: Product 1 3.00 1.00 0.25 Product 2 2.00 2.50 0.25 Product 3 1.50 2.00 0.25 During the next production period the labor-hours available are 450 in department A, 350 in department B, and 50 in department C. The profit contributions per unit are $28 for product 1, $30 for product 2, and $25 for product 3. (a) Formulate a linear programming model for maximizing total profit contribution. If the constant is "1" it must be entered in the box. If required, round your answers to two decimal places. Let P-units of product i produced Max $ s.t. P2 + P3 P2Select your answer P1+ P2+ P3Select your answer - v Select your answer- P1+ Pa + P1, P2P320 (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? Product 1 Product 2 Product 3 Amount to Produce Profit () After evaluating the sclution abtained in part(b,one of the production supervisors nated that production setup costs had not been taken into accounit. She noted that setup costs are $600 far product 1, $550 for praduct 2, and $400 for product 3. If the solution daveloped in part (b) is to be used, what is the total profit contribution after taking into account the setup costs? (d) Management realized that the optimal product mix, taking setup costs into account, might be different frorm the one recommended in part (b).Farmulate a mixed integer linear pragram that takes setup costs pravided in part (c) into account. Management also stated that we should not consider making more than 175 units of praduct 1, 150 units af product 2, ar 140 units of product 3. What are the new objective functian and additianal equation constraints? If the constant is "1 it must be entered in the box Let Y is one if any quantity af product i is praduced and zero otherwise. Max Pi+ th! Y2 s.t Gselect your answer . -]Ya P1 PzSelect your answer Select your answer P:, P2, P 2 0 (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). If required, round your answers to nearest whole number. If your answer is zero enter Product 1 Product 2 Product 3 Amount to Produce Updated Profit