Question Solved1 Answer 3) A chemical manufacturing firm has discontinued production of a certain unprofitable product line. This has created considerable excess production capacity on the three exist- ing batch production facilities. Management is considering devoting this excess capacity to one or more of three new products: Call them products 1, 2, and 3. The available capac- ity on the existing units that might limit output is summarized in the following table: Unit Available time (l/week) A B с 20 10 5 Each of the three new products requires the following processing time for completion: Productivity (h/batch) Unit Product 1 Product 2 Product 3 А 0.8 0.2 0.3 B с 0.2 0.1 The sales department indicates that the sales potential for products 1 and 2 exceeds the maximum production rate and that the sales potential for product 3 is 20 batches per week. The profit per batch is $20, $6, and $8, respectively, on products 1, 2, and 3. Formulate a linear programming model for determining how much of each prod- uct the firm should produce to maximize profit. 0.4 0,3

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Transcribed Image Text: 3) A chemical manufacturing firm has discontinued production of a certain unprofitable product line. This has created considerable excess production capacity on the three exist- ing batch production facilities. Management is considering devoting this excess capacity to one or more of three new products: Call them products 1, 2, and 3. The available capac- ity on the existing units that might limit output is summarized in the following table: Unit Available time (l/week) A B с 20 10 5 Each of the three new products requires the following processing time for completion: Productivity (h/batch) Unit Product 1 Product 2 Product 3 А 0.8 0.2 0.3 B с 0.2 0.1 The sales department indicates that the sales potential for products 1 and 2 exceeds the maximum production rate and that the sales potential for product 3 is 20 batches per week. The profit per batch is $20, $6, and $8, respectively, on products 1, 2, and 3. Formulate a linear programming model for determining how much of each prod- uct the firm should produce to maximize profit. 0.4 0,3
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Transcribed Image Text: 3) A chemical manufacturing firm has discontinued production of a certain unprofitable product line. This has created considerable excess production capacity on the three exist- ing batch production facilities. Management is considering devoting this excess capacity to one or more of three new products: Call them products 1, 2, and 3. The available capac- ity on the existing units that might limit output is summarized in the following table: Unit Available time (l/week) A B с 20 10 5 Each of the three new products requires the following processing time for completion: Productivity (h/batch) Unit Product 1 Product 2 Product 3 А 0.8 0.2 0.3 B с 0.2 0.1 The sales department indicates that the sales potential for products 1 and 2 exceeds the maximum production rate and that the sales potential for product 3 is 20 batches per week. The profit per batch is $20, $6, and $8, respectively, on products 1, 2, and 3. Formulate a linear programming model for determining how much of each prod- uct the firm should produce to maximize profit. 0.4 0,3
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Sol:Maximise f=6x+7ySubjecfed to 7x+6y <= 42=>7x+6y+S_(1)=42[S_(1) >= 0]{:[5x+9y <= 45=>5x+9y+S_(2)=45[S_(2) >= 0]],[x-y <= 4=>x-y+s_(2)=4[S_(3) >= 0]],[x⩾0","y >= 0]:}No. of Varlables (n)=5 [2 Decision + 3slack]No. of constraints n=3Maximise delta=6x+7y+0xxs_(1)+0xxs_(2) toxs _(3){:[7x+6y+s_(1)+0xxs_(2)+0xxs_(3)=42],[5x+9y+0xxs_(1)+s_(2)+0xxs_(3)=45],[x-y+0xxs_(1)+0xxs_(2)+s_(3)=4]:}No. of basic Variables n= ... See the full answer