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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. Product 2 Product 3 Department Product 1 A s.t. B с 1.50 2.00 0.25 3.00 1.00 0.25 2.00 Department A 1.5P₁ +3P2+2P3 ≤450 Department B2P₁ + P₂ +2.5P3 ≤ 350 Department c 0.25p₁ +0.25P₂ +0.25p3 ≤ 50 P1, P₂, P3 20 2.50 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, $27 for product 2, and $29 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 25P₁ +27P +29P₂ 0.25

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 3 Department Product 1 A s.t. B с 1.50 2.00 0.25 3.00 1.00 0.25 2.00 Department A 1.5P₁ +3P2+2P3 ≤450 Department B2P₁ + P₂ +2.5P3 ≤ 350 Department c 0.25p₁ +0.25P₂ +0.25p3 ≤ 50 P1, P₂, P3 20 2.50 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, $27 for product 2, and $29 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 25P₁ +27P +29P₂ 0.25

College Algebra
College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter5: Systems Of Equations And Inequalities
Section5.2: Systems Of Linear Equations In Several Variables
Problem 46E
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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 s.t. A B C Department A Department B 1.5P1 1.50 2P₁ + 1 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 $25 for product 1, $27 for product 2, and $29 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 25P₁+27P₂+29P 3 0.25 +3P2 +2P3 ≤ 450 P2 +2.5P3 ≤ 350 2.00 Department c 0.25p₁ +0.25P2 +0.25p3 ≤ 50 P1, P2, P320 2.50 0.25
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. Department Product 1 Product 2 Product 3 s.t. A B C Department A Department B 1.5P1 1.50 2P₁ + 1 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 $25 for product 1, $27 for product 2, and $29 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 25P₁+27P₂+29P 3 0.25 +3P2 +2P3 ≤ 450 P2 +2.5P3 ≤ 350 2.00 Department c 0.25p₁ +0.25P2 +0.25p3 ≤ 50 P1, P2, P320 2.50 0.25
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