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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.

Elementary Geometry for College Students
Elementary Geometry for College Students
6th Edition
ISBN:9781285195698
Author:Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:Daniel C. Alexander, Geralyn M. Koeberlein
ChapterA: Appendices
SectionA.1: Algebraic Expressions
Problem 1E: Name the four parts of a mathematical system. HINT: See Section 1.3
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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.

 

startup cost marginal income 1 $50 000 $70 Product 2 $40 000 $60 3 $70 000 $90 4 $60 000 $80
Transcribed Image Text:startup cost marginal income 1 $50 000 $70 Product 2 $40 000 $60 3 $70 000 $90 4 $60 000 $80
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