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
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...
Related questions
Question
![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).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5e07b399-2e24-4347-9303-782c80c8171b%2Fe8637a83-93a9-454f-a36e-e4a973225937%2Fdzwjv7_processed.png&w=3840&q=75)
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).
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 5 images
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Recommended textbooks for you
![Practical Management Science](https://www.bartleby.com/isbn_cover_images/9781337406659/9781337406659_smallCoverImage.gif)
Practical Management Science
Operations Management
ISBN:
9781337406659
Author:
WINSTON, Wayne L.
Publisher:
Cengage,
![Operations Management](https://www.bartleby.com/isbn_cover_images/9781259667473/9781259667473_smallCoverImage.gif)
Operations Management
Operations Management
ISBN:
9781259667473
Author:
William J Stevenson
Publisher:
McGraw-Hill Education
![Operations and Supply Chain Management (Mcgraw-hi…](https://www.bartleby.com/isbn_cover_images/9781259666100/9781259666100_smallCoverImage.gif)
Operations and Supply Chain Management (Mcgraw-hi…
Operations Management
ISBN:
9781259666100
Author:
F. Robert Jacobs, Richard B Chase
Publisher:
McGraw-Hill Education
![Practical Management Science](https://www.bartleby.com/isbn_cover_images/9781337406659/9781337406659_smallCoverImage.gif)
Practical Management Science
Operations Management
ISBN:
9781337406659
Author:
WINSTON, Wayne L.
Publisher:
Cengage,
![Operations Management](https://www.bartleby.com/isbn_cover_images/9781259667473/9781259667473_smallCoverImage.gif)
Operations Management
Operations Management
ISBN:
9781259667473
Author:
William J Stevenson
Publisher:
McGraw-Hill Education
![Operations and Supply Chain Management (Mcgraw-hi…](https://www.bartleby.com/isbn_cover_images/9781259666100/9781259666100_smallCoverImage.gif)
Operations and Supply Chain Management (Mcgraw-hi…
Operations Management
ISBN:
9781259666100
Author:
F. Robert Jacobs, Richard B Chase
Publisher:
McGraw-Hill Education
![Business in Action](https://www.bartleby.com/isbn_cover_images/9780135198100/9780135198100_smallCoverImage.gif)
![Purchasing and Supply Chain Management](https://www.bartleby.com/isbn_cover_images/9781285869681/9781285869681_smallCoverImage.gif)
Purchasing and Supply Chain Management
Operations Management
ISBN:
9781285869681
Author:
Robert M. Monczka, Robert B. Handfield, Larry C. Giunipero, James L. Patterson
Publisher:
Cengage Learning
![Production and Operations Analysis, Seventh Editi…](https://www.bartleby.com/isbn_cover_images/9781478623069/9781478623069_smallCoverImage.gif)
Production and Operations Analysis, Seventh Editi…
Operations Management
ISBN:
9781478623069
Author:
Steven Nahmias, Tava Lennon Olsen
Publisher:
Waveland Press, Inc.