The Progressive Company's research and development division is in the process of developing four lines of potential new products. Management must decide which of these four products to manufacture and at what levels. You have asked the OI department to formulate a mathematical programming model to find the most profitable mix of products. The start-up of the manufacture of any product is associated with a substantial cost, which is given in the first line of the table. The management objective is to find the product mix that maximizes total profit (total net income minus fixed costs). Define the continuous decision variables x1, x2, x3, and x4 as the production levels of products 1, 2, 3, and 4. By company policy, management has imposed the following restrictions on these variables: 1. At most, only two of these products should be produced. 2. Either product 3 or 4 can be produced only if product 1 or 2 is produced. 3. Either 5x1 1 3x2 1 6x3 1 4x4 # 6,000 or 4x1 1 6x2 1 3x3 1 5x4 # 6,000. a) Introduce auxiliary binary variables to formulate a mixed BIM model of this problem. b) Use the computer to solve this model.
The Progressive Company's research and development division is in the process of developing four lines of potential new products. Management must decide which of these four products to manufacture and at what levels. You have asked the OI department to formulate a mathematical programming model to find the most profitable mix of products.
The start-up of the manufacture of any product is associated with a substantial cost, which is given in the first line of the table. The management objective is to find the product mix that maximizes total profit (total net income minus fixed costs).
Define the continuous decision variables x1, x2, x3, and x4 as the production levels of products 1, 2, 3, and 4. By company policy, management has imposed the following restrictions on these variables:
1. At most, only two of these products should be produced.
2. Either product 3 or 4 can be produced only if product 1 or 2 is produced.
3. Either 5x1 1 3x2 1 6x3 1 4x4 # 6,000 or 4x1 1 6x2 1 3x3 1 5x4 # 6,000.
a) Introduce auxiliary binary variables to formulate a mixed BIM model of this problem.
b) Use the computer to solve this model.
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