setups costs are 370, 590, 580

Post by **answerhappygod** » Wed Jul 06, 2022 6:34 pm

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Hart Manufacturing makes three products. Each product requires manufacturing operations in three departments A, B, and C. The laber-hour requirements, by department, we as follows Department Product 1 Product 2 Product 3 A 3.00 G 1.00 1.50 st. 2.00 Department A 1.5P+3P₂+2P ≤ 450 Department 2+1₂+2.5P ≤ 350 Department c 25₁ +25₂ +25P3 ≤50 PPP 20 2.00 During the best production period, the labor hours available are 450 in department A, 350 in department 0, and 30 in department C. The profit contributions per unit we 524 for product 1, $17 hir product 2, and 12 for product 3 (a) Formulate a linear programining model for maximizning total profit contribution. (Let P,- units of product/produced, for /1,2,3) Max 24P +27P,+28P 2.50 60.80.60 0.25 (b) Solve the lineer program formulated in sort (a). How much of each product should be produced, and what is the projected total profit contribution on dolles? with profit 55220

(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 $370 for product 1. $500 for product 2, and $300 for product 3. If the solution developed in part (b) is to be used, what is the total prefit contribution (in dollar) after taking into account the setup costs? $ (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-edeger inear program that takes setup costs into account Management also stated that we should not consider making more than 140 usits of product 1, 145 units of product 2, or 100 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 / is produced and zero otherwise, for/=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 near program? St. units of Product t produced. units of Product 2 produced units of Product 3 produced PP20 YYY-0.1 (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 pruht (in dollars) contribution? with proft $ (P₁ P₂P₁ ₁₂ Yg).

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 2 Product 31 Department Product I 1.50 S.I. A B C 2.00 0.25 3.00 1.00 0.25 2.00 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 $24 for product 1, $27 for produm $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.) Max 24P₁ +27P,+28Pa Department A 1.5P+3P₂ +2P3 ≤450 Department B2P₁+1P₂ +2.5P3 ≤ 350 Department c-25P₁ +25P₂ + 25P3 ≤ 50 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 P₂) - 60.80.60 with profit $ 5220

(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 $370 for product 1, $590 for product 2, and $500 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? (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 100 units of product 1, 145 units of product 2, or 160 units of product 3. (Let P. units of product i produced and r, be the 0-1 variable that is one if any quantity of product iis 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 near program? units of Product 1 produced i units of Product 2 produced units of Product 3 produced P₁ Pg Pg 2 0; YjYgY₂ -0,1 (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 (in dollars) contribution? with profit S (P₂ -([