# There are three factories on the Momiss River: 1, 2, and 3. Each emits two types of pollutants,…

There are three factories on the Momiss River: 1, 2, and 3.

Each emits two types of pollutants, labeled P1 and P2,

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 ton processed reduces the amount of P1 by 0.10 ton and the

amount of P2 by 0.45 ton. It costs $10 to process a ton of factory 2

waste, and each ton processed will reduce the amount of P1 by 0.20 ton and the

amount of P2 by 0.25 ton. It costs $20 to process a ton of factory 3

waste, and each ton processed will reduce

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There are three factories on the Momiss River: 1, 2, and 3.

Each emits two types of pollutants, labeled P1 and P2,

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 ton processed reduces the amount of P1 by 0.10 ton and the

amount of P2 by 0.45 ton. It costs $10 to process a ton of factory 2

waste, and each ton processed will reduce the amount of P1 by 0.20 ton and the

amount of P2 by 0.25 ton. It costs $20 to process a ton of factory 3

waste, and each ton processed will reduce the amount of P1 by 0.40

ton and the amount of P2 by 0.30 ton. The state wants to reduce the

amount of P1 in the river by at least 30 tons and the amount of P2by

at least 40 tons.

a. Use Solver to determine how to minimize the cost of

reducing pollution by the desired amounts.

b. Are the LP assumptions (proportionality, additivity,

divisibility) reasonable in this problem?

c. Suppose you want to investigate the effects of increases

in the minimal reductions required by the state. Specifically, you want to see

what happens to the amounts of waste processed at the three factories and the

total cost if both requirements (currently 30 and 40 tons, respectively) are

increased by the same percentage. Revise your model so that you can use

SolverTable to investigate these changes when the percentage increase varies

from 10% to 100% in increments of 10%. Do the amounts processed at the three

factories and the total cost change in a linear manner?

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