(1) There are currently three permitted Marcellus shale hydro-fracking sites between Fairmont, WV and Point Marion, PA which are adjacent to the Monongahela River.
Each permitted site emits 15,000 tons of waste annually thereby discharging two types of pollutants (A and B) into the river.
If the waste from each site is filtered using technologies developed at the Water Research Institute at WVU, the pollution to the river can be reduced.
It costs $15 per ton to filter water from site one, and each ton filtered reduces the amount of pollutant A by 0.10 ton and the amount of pollutant B by 0.45 ton.
It costs $10 per ton to filter waste from site two, and each ton filtered will reduce the amount of pollutant A by 0.20 ton and the amount of pollutant B by 0.25 ton.
It costs $20 per ton to filter waste from site three, and each ton processed will reduce the amount pollutant A by 0.40 ton and the amount of pollutant B by 0.30 ton.
The WVDEP wants to reduce the amount of pollutant A in the river by at least 30 tons and the amount of pollutant B in the river by at least 40 tons.
- Formulate a linear programming problem that will minimize the annual cost of reducing pollution by the desired amounts.
- List and describe the assumptions of linear programming.
- Do you think that these assumptions are reasonable for this problem? Explain why or why not.