Problem 2 The AB manufacturing company has two kinds of products: A and B. They earn $180 profit for each Product A and $90 profit for each Product B. To produce Products A and B, the company needs three resources: Q, R, S. Each unit of Product A consumes 6 units of Resource Q and 2 units of Resource R. Each unit of Product B consumes 8 units of Resource Q and 3 units of Resource S. The AB manufacturing company only can use 48 units of Q, 12 units of R and 12 units of S per day. Resource Product A Product B Resource Available Q 6. 8 48 R 12 S 3 12 Profit per unit 180 90 1. Formulate a linear program and use simplex algorithm to solve it. 2. Write downm a linear programming model to determine the minimum total amount the insur- ance company should pay to AB manufacturing when they lose all the available resource. (Hint: consider the relationship between this LP for the insurance company and the original LP for the AB company). 3. What are the shadow prices for each resource? Which is the most “scarce" resource for AB manufacturing? 4. How much can you increase/decrease the resource level of Q while the current optimal solution stays optimal? 5. How much can you increase/decrease the resource level of R while the current optimal solution stays optimal? 6. How much can you increase/decrease the resource level of S while the current optimal solution stays optimal?
Problem 2 The AB manufacturing company has two kinds of products: A and B. They earn $180 profit for each Product A and $90 profit for each Product B. To produce Products A and B, the company needs three resources: Q, R, S. Each unit of Product A consumes 6 units of Resource Q and 2 units of Resource R. Each unit of Product B consumes 8 units of Resource Q and 3 units of Resource S. The AB manufacturing company only can use 48 units of Q, 12 units of R and 12 units of S per day. Resource Product A Product B Resource Available Q 6. 8 48 R 12 S 3 12 Profit per unit 180 90 1. Formulate a linear program and use simplex algorithm to solve it. 2. Write downm a linear programming model to determine the minimum total amount the insur- ance company should pay to AB manufacturing when they lose all the available resource. (Hint: consider the relationship between this LP for the insurance company and the original LP for the AB company). 3. What are the shadow prices for each resource? Which is the most “scarce" resource for AB manufacturing? 4. How much can you increase/decrease the resource level of Q while the current optimal solution stays optimal? 5. How much can you increase/decrease the resource level of R while the current optimal solution stays optimal? 6. How much can you increase/decrease the resource level of S while the current optimal solution stays optimal?
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
100%
Is one question, with parts. Please answer all if you can, Please do it by hand. Please do it by HAND please. Take your time, but do it by hand please.
Transcribed Image Text:Problem 2 The AB manufacturing company has two kinds of products: A and B. They earn
$180 profit for each Product A and $90 profit for each Product B. To produce Products A and B,
the company needs three resources: Q, R, S. Each unit of Product A consumes 6 units of Resource
Q and 2 units of Resource R. Each unit of Product B consumes 8 units of Resource Q and 3 units
of Resource S. The AB manufacturing company only can use 48 units of Q, 12 units of R and 12
units of S per day.
Resource
Product A
Product B
Resource Available
Q
6.
48
R.
12
3
12
Profit per unit
180
90
1. Formulate a linear program and use simplex algorithm to solve it.
2. Write down a linear programming model to determine the minimum total amount the insur-
ance company should pay to AB manufacturing when they lose all the available resource.
(Hint: consider the relationship between this LP for the insurance company and the original
LP for the AB company).
3. What are the shadow prices for each resource? Which is the most "scarce" resource for AB
manufacturing?
4. How much can you increase/decrease the resource level of Q while the current optimal solution
stays optimal?
5. How much can you increase/decrease the resource level of R while the current optimal solution
stays optimal?
6. How much can you increase/decrease the resource level of S while the current optimal solution
stays optimal?
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 5 steps with 7 images
Recommended textbooks for you
Practical Management Science
Operations Management
ISBN:
9781337406659
Author:
WINSTON, Wayne L.
Publisher:
Cengage,
Operations Management
Operations Management
ISBN:
9781259667473
Author:
William J Stevenson
Publisher:
McGraw-Hill Education
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
Operations Management
ISBN:
9781337406659
Author:
WINSTON, Wayne L.
Publisher:
Cengage,
Operations Management
Operations Management
ISBN:
9781259667473
Author:
William J Stevenson
Publisher:
McGraw-Hill Education
Operations and Supply Chain Management (Mcgraw-hi…
Operations Management
ISBN:
9781259666100
Author:
F. Robert Jacobs, Richard B Chase
Publisher:
McGraw-Hill Education
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…
Operations Management
ISBN:
9781478623069
Author:
Steven Nahmias, Tava Lennon Olsen
Publisher:
Waveland Press, Inc.