Problem 2 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: Start-up cost 1 Product $70 2 3 $50,000 $40,000 $70,000 $60,000 $60 4 Marginal revenue Let continuous variables 1, 2, 3, 4 be the production levels of product 1,2,3 and 4, respec- tively, and let binary variables y₁, 92, 93, 94 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 2 is produced, then neither product 3 nor product 4 can be produced. Either 5x1 + 3x2 +6x3+4x4≤ 6000 or 4x₁ + 6x2 + 3x3 + 5x4≤ 6000. Formulate an integer programming model for the problem. (No need to solve it) $90 $ 80

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Problem 2 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:
Start-up cost
Marginal revenue
1
2
$ 70
Product
3
$50,000 $40,000 $70,000 $60,000
$ 60
4
$ 90
$ 80
Let continuous variables x₁, x2, 3, 4 be the production levels of product 1,2,3 and 4, respec-
tively, and let binary variables y₁, 92, 93, 94 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 2 is produced, then neither product 3 nor product 4 can be produced.
• Either 5x₁ + 3x2 + 6x3 + 4x4 ≤ 6000 or 4x₁ + 6x2 + 3x3 + 5x4≤ 6000.
Formulate an integer programming model for the problem. (No need to solve it)
Transcribed Image Text:Problem 2 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: Start-up cost Marginal revenue 1 2 $ 70 Product 3 $50,000 $40,000 $70,000 $60,000 $ 60 4 $ 90 $ 80 Let continuous variables x₁, x2, 3, 4 be the production levels of product 1,2,3 and 4, respec- tively, and let binary variables y₁, 92, 93, 94 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 2 is produced, then neither product 3 nor product 4 can be produced. • Either 5x₁ + 3x2 + 6x3 + 4x4 ≤ 6000 or 4x₁ + 6x2 + 3x3 + 5x4≤ 6000. Formulate an integer programming model for the problem. (No need to solve it)
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