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Problem: There are three factories on the Momiss River. 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 $1500 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 $2500 to process a ton of factory 2 waste, and each ton processed reduces the amount of P1 by 0.20 ton and the amount of P2 by 0.25 ton. It costs $3000 to process a ton of factory 3 waste, and each ton processed reduces the amount of P1 by 0.40 ton and the amount of P2 by 0.50 ton. The state wants to reduce the amount of P1 in the river by at least 125 tons and the amount of P2 by at least 175 tons.

a. Use Solver to determine how to minimize the cost of reducing pollution by the desired amounts. Are the LP assumptions (proportionality, additivity, divisibility) reasonable in this problem?

b. Use SolverTable to investigate the effects of increases in the minimal reductions required by the state. Specifically, see what happens to the amounts of waste processed at the three factories and the total cost if both requirements (currently 125 and 175 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?

A 1 River pollutants 2 3 Factory 4 cost per ton 5 P1 Reduced 6 P2 Reduced 8 Units Produced 9 10 Total P1 Reduced 11 Total P2 Reduced 12 13 total cost 14 15 16 3.. 03: 67890 17 18 19 20 21 22 345 26 27 28 29 30 31 32 33 34 35 36 38 Ready B 1 $15 0.1 0.45 0.00 >= 0x Answer Report 1 C 2 $10 0.2 0.25 D 3 $20 0.4 0.3 30 40 Sensitivity Report 1 Ans