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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 A 3.00 B 1.00 С 0.25 Department A 1.50 Department 8 2.00 0.25 2.00 During the next production period, the laber-hours available are 450 in department A, 350 in department 8, and 50 in department C. The profit contributions per unit are $24 for product 1, 827 for product 2, and $29 for product 3. (a) Formulate a linear programming model for maximizing total profit contribution. (Let P, units of product/produced, for/ 1,2,3) Max 24p +27p+29p3 + 2.50 0.25 Department C P1 P₂ P₂ 20 (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, P₂P) - with profit s (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 $400 the total profit contribition in Bars) after taking into account the
(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 $400 for product 1, $530 for product 2, and $600 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? S (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 Snear program that takes setup costs into account. Management also stated that we should not consider making more than 145 units of product 1, 175 units of product 2, or 185 units of product 3 (Let Punits of product / 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 linear program? S.I. units of Product 1 produced units of Product 2 produced units of Product 3 produced P₁ P₂ PgZ0; V₁ Y₂Y-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 (P₁ P₂ P₂ V₁ Y2Y3) 1 Mond Hein? Read 11