Question Solved1 Answer 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 (h/week) A 20 B 20 С 05 Each of the three new products requires the following processing time for completion: Productivity (h/batch) Unit Product 1 Product 2 Product 3 A 0.8 0.2 0.3 B. 0.4 0.3 с 0.1 0.2 The sales department indicates that the sales for products 1 and 2exceeds 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.How much of each product should be produced to maximize profits of the company? Formulate the objective function and constraints, but do not solve.

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Transcribed Image Text: 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 (h/week) A 20 B 20 С 05 Each of the three new products requires the following processing time for completion: Productivity (h/batch) Unit Product 1 Product 2 Product 3 A 0.8 0.2 0.3 B. 0.4 0.3 с 0.1 0.2 The sales department indicates that the sales for products 1 and 2exceeds 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.How much of each product should be produced to maximize profits of the company? Formulate the objective function and constraints, but do not solve.
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Transcribed Image Text: 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 (h/week) A 20 B 20 С 05 Each of the three new products requires the following processing time for completion: Productivity (h/batch) Unit Product 1 Product 2 Product 3 A 0.8 0.2 0.3 B. 0.4 0.3 с 0.1 0.2 The sales department indicates that the sales for products 1 and 2exceeds 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.How much of each product should be produced to maximize profits of the company? Formulate the objective function and constraints, but do not solve.
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Productividy (u/batoln)=> Here the aim is to maximise profit, so objective function will be the profit function of the plant for one week=> Note from 2 nd table that Prod2 Cait be produced in Unit C and Product 3 cant be produced in Unit B=> Let x_(A) be the no. of batches of Product one produced in Unit ALet X_(B) be the no. of batcher of product I produced in Unit B Let xc be the no. of batches of product I produced in Unitc Let Y_(A) be the no. of batches of product 2 produced in Unit A Let y_(B) be the no. of batcher f product 2 produced in Unit B Let 3A be the no. 3 p batches of product 3 produced in Unit A Let 3C be the no. of batches of product 3 produced in=> It is alio given that profit fo Product 1,2,3 are $20,$6,$8 respectively.hence the profit function of the compamy for one meekf=20(x_(A)+x_(B)+x_(C))+6(y_(A)+y_(B))+8(3A+3C)=> now coming to constraints, the time for each unit is limited. Weas also kn ... See the full answer