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 1. Formulate a linear program and use the 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
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
1. Formulate a linear program and use the 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
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