Question

1. Question There are three factories on the Momiss River. Each factory emits two types of pollutants 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 waste from factory 1, and each ton of factory 1 waste processed will reduce the amount of pollutant 1 by 0.10 ton and will reduce the amount of pollutant 2 by 0.45 ton. It costs $10 to process a ton of waste from factory 2, and each ton of factory 2 waste processed will reduce the amount of pollutant 1 by 0.20 ton and will reduce the amount of pollutant 2 by 0.25 ton. It costs $20 to process a ton of waste from factory 3, and each ton of factory 3 waste processed will reduce the amount of pollutant 1 by 0.40 ton and will reduce the amount of pollutant 2 by 0.30 ton. The state wishes to reduce the amount of pollutant 1 in the river by at least 30 tons, and the amount of pollutant 2 in the river by at least 40 tons. Formulate an LP that will minimize the cost of reducing pollution by the desired amounts.

2. Variables:- P1= amount of pollutant 1 in the waste give out by factory 1 Q1= amount of pollutant 1 in the waste given out by factory 2 R1= amount of pollutant 1 in the waste given out by factory 3 P2= amount of pollutant 2 in the waste given out by factory 1 Q2= amount of pollutant 2 in the waste given out by factory 2 R2= amount of pollutant 2 in the waste given out by factory 3

3. Objective :- Minimize cost of reducing pollution by the desired amount Z= 15(P1+P2)+10(Q1+Q2)+20(R1+R2) Constraints :- - 0.10P1+0.20Q1+0.40R1 >=30 - 0.45P2+0.25Q2+0.30R2 >= 40 - P1,P2,Q1,Q2,R1,R2>=0