The Research Development Division of the GOOD PRODUCTS COMPANY has developed three possible new products. However,...

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The Research Development Division of the GOOD PRODUCTS COMPANY has developed three possible new products. However, to avoid undue diversification of the company's product line, management has imposed the following restriction. Restriction: From the three possible new products, at most two should be chosen to be produced. The production cost per unit of each product would be essentially the same in the two plants. However, because of differences in their production facilities, the number of hours of production time needed per unit of each product might differ between two plants. Both plants are allowed for new product production. That is, each of these products may be produced in both plants at the same time. These data are given in the following table, along with other relevant information, including marketing estimates of the number of units of each product that could be sold per week if it is produced. The objective is to maximize total profit. Production Time Used for Each Unit Produced Product 1 Product 2 Product 3 3 hours 4 hours 4 hours 6 hours 5 7 7 5 Plant 1 Plant 2 Unit profit Sales potential (a) Define all variables you need. (b) Formulate the objective function and constraints. 2 hours 2 hours 3 9 Production Time Available per Week 30 hours 40 hours (thouuands of dollars) (units per week) The Research Development Division of the GOOD PRODUCTS COMPANY has developed three possible new products. However, to avoid undue diversification of the company's product line, management has imposed the following restriction. Restriction: From the three possible new products, at most two should be chosen to be produced. The production cost per unit of each product would be essentially the same in the two plants. However, because of differences in their production facilities, the number of hours of production time needed per unit of each product might differ between two plants. Both plants are allowed for new product production. That is, each of these products may be produced in both plants at the same time. These data are given in the following table, along with other relevant information, including marketing estimates of the number of units of each product that could be sold per week if it is produced. The objective is to maximize total profit. Production Time Used for Each Unit Produced Product 1 Product 2 Product 3 3 hours 4 hours 4 hours 6 hours 5 7 7 5 Plant 1 Plant 2 Unit profit Sales potential (a) Define all variables you need. (b) Formulate the objective function and constraints. 2 hours 2 hours 3 9 Production Time Available per Week 30 hours 40 hours (thouuands of dollars) (units per week)

Answer rating: 100% (QA)

a Variables Let x1 be the number of units of Product 1 produced in Plant 1 Let x2 be the number of units of Product 2 produced in Plant 1 ... View the full answer