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Problem 1 The R& D division of the Progressive company has been developing 4 possible product lines. Management must make a decision on which of the 4 products will be produced and at what levels to maximize the profit. The start-up cost and marginal revenue for each product is given in the following table: Product 1 2 3 4 Start-up cost $50,000 $40,000 $70,000 $60,000 Marginal revenue $ 70 $ 60 $ 90 $ 80 Let continuous variables r1, x2, 13, X4 be the production levels of product 1,2,3 and 4, respec- tively, and let binary variables Y1, Y2, Y3; Y4 Control whether or not each product is produced at all. Suppose the manager has imposed the following constraints: • No more than two types of the products can be produced. • If neither product 1 nor product 2 is produced, then neither product 3 nor product 4 can be produced. • Either 5x1 + 3.x2 + 6x3 + 4x4 < 6000 or 4x1+ 6x2 + 3x3+ 5x4 < 6000. 1. Formulate an integer programming model for the problem. 2. Solve this model in Excel or Python.

Problem 1 The R& D division of the Progressive company has been developing 4 possible product lines. Management must make a decision on which of the 4 products will be produced and at what levels to maximize the profit. The start-up cost and marginal revenue for each product is given in the following table: Product 1 2 3 4 Start-up cost $50,000 $40,000 $70,000 $60,000 Marginal revenue $ 70 $ 60 $ 90 $ 80 Let continuous variables r1, x2, 13, X4 be the production levels of product 1,2,3 and 4, respec- tively, and let binary variables Y1, Y2, Y3; Y4 Control whether or not each product is produced at all. Suppose the manager has imposed the following constraints: • No more than two types of the products can be produced. • If neither product 1 nor product 2 is produced, then neither product 3 nor product 4 can be produced. • Either 5x1 + 3.x2 + 6x3 + 4x4 < 6000 or 4x1+ 6x2 + 3x3+ 5x4 < 6000. 1. Formulate an integer programming model for the problem. 2. Solve this model in Excel or Python.

Practical Management Science
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...
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Problem 1 The R& D division of the Progressive company has been developing 4 possible product lines. Management must make a decision on which of the 4 products will be produced and at what levels to maximize the profit. The start-up cost and marginal revenue for each product is given in the following table: Product 1 3 Start-up cost $50,000 $40,000 $70,000 $60,000 Marginal revenue $ 70 $ 60 $ 90 $ 80 Let continuous variables x1, x2, X3, X4 be the production levels of product 1,2,3 and 4, respec- tively, and let binary variables y1, Y2, Y3, Y4 control whether or not each product is produced at all. Suppose the manager has imposed the following constraints: • No more than two types of the products can be produced. • If neither product 1 nor product 2 is produced, then neither product 3 nor product 4 can be produced. • Either 5x1 + 3.x2 + 6x3 + 4x4 < 6000 or 4x1 + 6x2 +3x3 +5x4 < 6000. 1. Formulate an integer programming model for the problem. 2. Solve this model in Excel or Python.
Transcribed Image Text:Problem 1 The R& D division of the Progressive company has been developing 4 possible product lines. Management must make a decision on which of the 4 products will be produced and at what levels to maximize the profit. The start-up cost and marginal revenue for each product is given in the following table: Product 1 3 Start-up cost $50,000 $40,000 $70,000 $60,000 Marginal revenue $ 70 $ 60 $ 90 $ 80 Let continuous variables x1, x2, X3, X4 be the production levels of product 1,2,3 and 4, respec- tively, and let binary variables y1, Y2, Y3, Y4 control whether or not each product is produced at all. Suppose the manager has imposed the following constraints: • No more than two types of the products can be produced. • If neither product 1 nor product 2 is produced, then neither product 3 nor product 4 can be produced. • Either 5x1 + 3.x2 + 6x3 + 4x4 < 6000 or 4x1 + 6x2 +3x3 +5x4 < 6000. 1. Formulate an integer programming model for the problem. 2. Solve this model in Excel or Python.
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