Question Solved1 Answer Question 1 A chemical manufacturing firm has discontinued production of a certain unprofitable product line. This has created considerable excess production capacity on the three existing batch production facilities that operate separately. Management is considering devoting this excess capacity to one or more of three new products; call them products 1, 2, and 3. The available capacity on the existing units which might limit output is summarized in the following table: Unit Available time (hr/week) 20 B 10 A с 5 Each of the three new products requires the following processing time for completion: Unit Productivity (hr/batch) Product 1 Product 2 Product 3 A 0.8 0.2 0.3 B 0.4 с 0.2 0.1 0.3 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 would be $20, $6, and $8, respectively, on products 1, 2, and 3. If Xij be the number of batches of product i (i = 1, 2, 3) produced per week on unitj (j = A,B,C), formulate the objective function and constraints to maximize profits of the company. Do not solve the problem.

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Transcribed Image Text: Question 1 A chemical manufacturing firm has discontinued production of a certain unprofitable product line. This has created considerable excess production capacity on the three existing batch production facilities that operate separately. Management is considering devoting this excess capacity to one or more of three new products; call them products 1, 2, and 3. The available capacity on the existing units which might limit output is summarized in the following table: Unit Available time (hr/week) 20 B 10 A с 5 Each of the three new products requires the following processing time for completion: Unit Productivity (hr/batch) Product 1 Product 2 Product 3 A 0.8 0.2 0.3 B 0.4 с 0.2 0.1 0.3 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 would be $20, $6, and $8, respectively, on products 1, 2, and 3. If Xij be the number of batches of product i (i = 1, 2, 3) produced per week on unitj (j = A,B,C), formulate the objective function and constraints to maximize profits of the company. Do not solve the problem.
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Transcribed Image Text: Question 1 A chemical manufacturing firm has discontinued production of a certain unprofitable product line. This has created considerable excess production capacity on the three existing batch production facilities that operate separately. Management is considering devoting this excess capacity to one or more of three new products; call them products 1, 2, and 3. The available capacity on the existing units which might limit output is summarized in the following table: Unit Available time (hr/week) 20 B 10 A с 5 Each of the three new products requires the following processing time for completion: Unit Productivity (hr/batch) Product 1 Product 2 Product 3 A 0.8 0.2 0.3 B 0.4 с 0.2 0.1 0.3 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 would be $20, $6, and $8, respectively, on products 1, 2, and 3. If Xij be the number of batches of product i (i = 1, 2, 3) produced per week on unitj (j = A,B,C), formulate the objective function and constraints to maximize profits of the company. Do not solve the problem.
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Answer: Sol:Maximise f=6x+7ySubjected 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 +3 slack]No. of constraints n=3Maximise f=6x+7y+0xxs_(1)+0xxs_(2) toxs _(3){:[7x+6y+s_(1)+0xxs_(2)+0xxs_(3)=42],[5x+9y+0xxs_(1)+s_(2)+0 ... See the full answer