There are three factories on a river, each of which 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 $1000 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 $2000 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 0.30 ton. The state wants to reduce the amount of P1 in the river by at least 30 tons and the amount of P2 by at least 40 tons. [a] Determine the minimum cost of reducing pollution by the desired amounts. [b] 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 30 and 40 tons, respectively) are increased by the same percentage, Investigate these changes when the percentage increase varies from 10% to 90% in increments of 20%.
There are three factories on a river, each of which 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 $1000 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 $2000 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 0.30 ton. The state wants to reduce the amount of P1 in the river by at least 30 tons and the amount of P2 by at least 40 tons. [a] Determine the minimum cost of reducing pollution by the desired amounts. [b] 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 30 and 40 tons, respectively) are increased by the same percentage, Investigate these changes when the percentage increase varies from 10% to 90% in increments of 20%.
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