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 through 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. However, 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 tum means that the community will be subsidizing the mill's waste treatment at the city sewage treatment plant.

(a) Formulate an optimization model from the standpoint of the plant manager who is only interested in maximizing net profits (income less treatment-related costs) for the company.

(b) Formulate the problem as a multi objective program from the standpoint of the city council. which must set effluent discharge taxes in such a way as to prevent O\'c~­ subsidizing the plant's operation. but which also wants the plant lo remain fiscal!y healthy.