There are three factories on the Moniss River: 1, 2, and 3. Each emits two types of pollutants, labeled A and B, into the river. If the waste from each factory is processed, the pollution in the river...

There are three factories on the Moniss River: 1, 2, and 3. Each emits two types of pollutants, labeled A and B, into the river. If the waste from each factory is processed, the pollution in the river can be reduced.

• It costs $15 to process a ton of factory 1 waste, and each tone processed reduces the amount of A by 0.10 tons and the amount of B by 0.45 ton.


• It costs $14 to process a ton of factory 2 waste, and each ton processed will reduce the amount of A by 0.20 tons and the amount of B by 0.25 ton.


• It costs $12 to process a ton of factory 3 waste, and each ton processed will reduce the amount of A by 0.40 tons and the amount of B by 0.30 ton.


• The state wants to reduce the amount of A in the river by at least 25 tons and the amount of B by at least 30 tons. Furthermore, the total amount of A and B should be reduced by at least 65 tons. Also, the total amount of pollution to be processed cannot exceed 150 tons due to the technology limitation.

The state needs to decide how to minimize the cost of reducing pollution by the desired amounts wastes to be processed.

Questions:

1. Formulate this problem as an LP and work on the spreadsheet template provided to setup the model and solve it. Describe the 3-step formulation and the optimal solution.


2. Obtain the “Sensitivity” report from Solver. What is the shadow price of pollutant B reduction amount? How would you interpret this number?