The rolling mill in a large steel plant generates two types of water wastes: pickling waste and process water. If these wastes are discharged directly into the local city sewer without treatment, they are subject to an effluent tax. Alternatively, the plant operates a treatment facility capable of removing 90% of the pollutants from the waste streams. In this case the pickling wastes require pre-treatment (neutralization) before being processed thro ugh the plant's treatment facility.
The local municipality controls the effluent tax on untreated wastes entering city sewers; the higher the effluent tax, the more wastes the steel mill will treat on site. How-ever, this could cause a decrease in the plant’s productivity that could directly affect the economy of the community. The lower the effluent tax, the less waste the plant will treat and production will be higher. But this in turn means that the community will be subsidizing the mill's waste treatment at the city sewage treatment plant.
Let: x1 = tons of steel to be manufactured per day
x2 = volume of pickle waste (gallons) treated per day
x3 = volume of process water (gallons) treated per day
Income from the production of steel = $25/ton
Pickle waste generated = 100 gallons/ton of steel
Process water generated = 1000 gallons/ton of steel
Pre-treatment cost = $.02/thousand gallons treated
Treatment cost = $.10/thousand gallons treated
Pre-treatment capacity = 2,000,000 gallons/day
Treatment capacity = 50,000,000 gallons/day
Treatment efficiency = 90% (both wastes)
Tax all untreated pickle waste = $0.15/thousand gallons
Tax on untreated process water = $0.05/thousand gallons
Limit on pickle waste discharge to city sewer = 500,000 gallons/day
Limit on process water discharge to city sewer = 10,000,000 gallons/day.
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