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Note: In problems 1, 2, and 3, the constraints are the same. This means the feasible regions are the same. The only difference is in the objective function. When you solve the three problems, go back and study the coefficients of the variables in the objective function of each problem. These represent the profit contributions of products X₁ and x2 in each problem. Try to understand intuitively why the optimal solution is changing for each problem (at a different corner point).

Note: In problems 1, 2, and 3, the constraints are the same. This means the feasible regions are the same. The only difference is in the objective function. When you solve the three problems, go back and study the coefficients of the variables in the objective function of each problem. These represent the profit contributions of products X₁ and x2 in each problem. Try to understand intuitively why the optimal solution is changing for each problem (at a different corner point).

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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1) Max Z = x₁ + 3x2 s.t. 2x1 + 4x2 ≤ 14 6x1 + 2x2 ≤ 12 Xi≥ 0 2) Max Z = X₁ + X2 s.t. 2x1 +4x2 ≤ 14 6x1 + 2x2 ≤ 12 Xi ≥0 3) Max Z = 4x1 + x2 s.t. 2x1 + 4x2 ≤ 14 6x1+ 2x2 ≤ 12 Xi ≥ 0 Note: In problems 1, 2, and 3, the constraints are the same. This means the feasible regions are the same. The only difference is in the objective function. When you solve the three problems, go back and study the coefficients of the variables in the objective function of each problem. These represent the profit contributions of products x₁ and x2 in each problem. Try to understand intuitively why the optimal solution is changing for each problem (at a different corner point).
Transcribed Image Text:1) Max Z = x₁ + 3x2 s.t. 2x1 + 4x2 ≤ 14 6x1 + 2x2 ≤ 12 Xi≥ 0 2) Max Z = X₁ + X2 s.t. 2x1 +4x2 ≤ 14 6x1 + 2x2 ≤ 12 Xi ≥0 3) Max Z = 4x1 + x2 s.t. 2x1 + 4x2 ≤ 14 6x1+ 2x2 ≤ 12 Xi ≥ 0 Note: In problems 1, 2, and 3, the constraints are the same. This means the feasible regions are the same. The only difference is in the objective function. When you solve the three problems, go back and study the coefficients of the variables in the objective function of each problem. These represent the profit contributions of products x₁ and x2 in each problem. Try to understand intuitively why the optimal solution is changing for each problem (at a different corner point).
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