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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 3.00 Max A s.t. B с Department A Department B 1.50 Department C P₁ P₂ P3 20 2.00 0.25 1.00 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 $23 for product 1, $27 for product 2, and $28 for product 3. (a) Formulate a linear programming model for maximizing total profit contribution. (Let P, = units of product i produced, for i = 1, 2, 3.) 0.25 2.00 2.50 0.25 (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 (in dollars)? (P₁ P₂ P3) = with 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 $380 for product 1, $500 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 (in dollars) after taking into account the setup costs? $

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 3.00 Max A s.t. B с Department A Department B 1.50 Department C P₁ P₂ P3 20 2.00 0.25 1.00 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 $23 for product 1, $27 for product 2, and $28 for product 3. (a) Formulate a linear programming model for maximizing total profit contribution. (Let P, = units of product i produced, for i = 1, 2, 3.) 0.25 2.00 2.50 0.25 (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 (in dollars)? (P₁ P₂ P3) = with 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 $380 for product 1, $500 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 (in dollars) after taking into account the setup costs? $

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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(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 145 units of product 1, 155 units of product 2, or 160 units of product 3. (Let P₁ = units of product i produced and y; be the 0-1 variable that is one if any quantity of product / 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, P320;Y₁ Y2Y3 = 0, 1 (e) Solve the mixed-integer linear program formulated in part (d). How much of each product should produced, and what (P₁1 P2 P31 Y ₁1 Y21 Y3) = ( with profit $ projected total profit (in ars) contribution?
Transcribed Image Text:(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 145 units of product 1, 155 units of product 2, or 160 units of product 3. (Let P₁ = units of product i produced and y; be the 0-1 variable that is one if any quantity of product / 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, P320;Y₁ Y2Y3 = 0, 1 (e) Solve the mixed-integer linear program formulated in part (d). How much of each product should produced, and what (P₁1 P2 P31 Y ₁1 Y21 Y3) = ( with profit $ projected total profit (in ars) contribution?
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. Max Department Product 1 Product 2 Product 3 s.t. A B с Department A Department B 1.50 Department C P₁, P2, P320 P1¹ 2.00 0.25 3.00 1.00 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 $23 for product 1, $27 for product 2, and $28 for product 3. (a) Formulate a linear programming model for maximizing total profit contribution. (Let P; = units of product i produced, for i = 1, 2, 3.) 0.25 2.00 2.50 0.25 (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 (in dollars)? (P₁, P₂, P3)-([ with 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 $380 for product 1, $500 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 (in dollars) after taking into account the setup costs? $
Transcribed Image Text: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. Max Department Product 1 Product 2 Product 3 s.t. A B с Department A Department B 1.50 Department C P₁, P2, P320 P1¹ 2.00 0.25 3.00 1.00 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 $23 for product 1, $27 for product 2, and $28 for product 3. (a) Formulate a linear programming model for maximizing total profit contribution. (Let P; = units of product i produced, for i = 1, 2, 3.) 0.25 2.00 2.50 0.25 (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 (in dollars)? (P₁, P₂, P3)-([ with 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 $380 for product 1, $500 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 (in dollars) after taking into account the setup costs? $
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