Please help in solving Part (e) 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:DepartmentProduct 23.00AB1.00с0.25s.t.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 $25 for product 1, $28 for product 2, and $30 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 P₁ = units of product i producedMax S25 P₁ + $1.5 P₁+2 P₁+.25 P₁+P₁, P2, P3 2 0 and integerAmount to ProduceMax SProduct 11.502.000.25s.t.28 P₂ + $Amount to Produce3 P₂ +1 P2 +.25 P₂ +Updated Profit $+6030 P3802 P3 S2.5 P3 S.25 P3 S(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 328 P2 + $Product 32.002.500.25Profit $ 5540(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 $550 for product 1, $400 for product 2, and $600 for product 3. If the solution developed in part (b) is to be used, what is the total profit contributionafter taking into account the setup costs?$603990(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 provided in part (c) into account. Management also stated that we should not consider making more than 175 units of product1, 150 units of product 2, or 140 units of product 3. What are the new objective function and additional equation constraints?If the constant is "1" it must be entered in the box.Let Yi is one if any quantity of product i is produced and zero otherwise.25 P₁$30 P3 - $VVVVV175 V₁V450150 V₂140 Y33501 P₁ S1 P₂ S1 P3 SP1, P2, P3 2 0 and integer(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 "0".Product 1 Product 2 Product 350550 Y₁ - $ 400 Y₂ - $600 Y3

Question

Please help in solving Part (e) 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:DepartmentProduct 23.00AB1.00с0.25s.t.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 $25 for product 1, $28 for product 2, and $30 for product 3.(a) Formulate a linear programming model for maximizing total profit contribution.If the constant is &#34;1&#34; it must be entered in the box. If required, round your answers to two decimal places.Let P₁ = units of product i producedMax S25 P₁ + $1.5 P₁+2 P₁+.25 P₁+P₁, P2, P3 2 0 and integerAmount to ProduceMax SProduct 11.502.000.25s.t.28 P₂ + $Amount to Produce3 P₂ +1 P2 +.25 P₂ +Updated Profit $+6030 P3802 P3 S2.5 P3 S.25 P3 S(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 328 P2 + $Product 32.002.500.25Profit $ 5540(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 $550 for product 1, $400 for product 2, and $600 for product 3. If the solution developed in part (b) is to be used, what is the total profit contributionafter taking into account the setup costs?$603990(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 provided in part (c) into account. Management also stated that we should not consider making more than 175 units of product1, 150 units of product 2, or 140 units of product 3. What are the new objective function and additional equation constraints?If the constant is &#34;1&#34; it must be entered in the box.Let Yi is one if any quantity of product i is produced and zero otherwise.25 P₁$30 P3 - $VVVVV175 V₁V450150 V₂140 Y33501 P₁ S1 P₂ S1 P3 SP1, P2, P3 2 0 and integer(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 &#34;0&#34;.Product 1 Product 2 Product 350550 Y₁ - $ 400 Y₂ - $600 Y3

Accepted Answer

Note:You have asked only for part e. I have answered only them Formulation:Decision Variables:P1=…