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. 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 ResourceQ and 2 units of Resource R. Each unit of Product B consumes 8 units of Resource Q and 3 unitsof Resource S. The AB manufacturing company only can use 48 units of Q, 12 units of R and 12units of S per day.ResourceProduct AProduct BResource AvailableQ6.48R.12312Profit per unit180901. 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 originalLP for the AB company).3. What are the shadow prices for each resource? Which is the most "scarce" resource for ABmanufacturing?4. How much can you increase/decrease the resource level of Q while the current optimal solutionstays optimal?5. How much can you increase/decrease the resource level of R while the current optimal solutionstays optimal?6. How much can you increase/decrease the resource level of S while the current optimal solutionstays optimal?

Note that, we could not generate a sensitivity report by hand and without a sensitivity report…

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?

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter4: Linear Programming Models

Section: Chapter Questions

Problem 73P