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(P1P2)10(Q1Q2)20(R1R2)
• Constraints -
• - 0.10P10.20Q10.40R1 gt30
• - 0.45P20.25Q20.30R2 gt 40
• - P1,P2,Q1,Q2,R1,R2gt0