# The Environmental Protection Agency (EPA) wants to restrict the amount of pollutants added by a company to the river water. The concentrations of phenol and nitrogen in the water are to be restricted to, respectively, P and N lbs. MG (million gallons) on a daily basis. The river has a flow of M MG/day. The company diverts a portion of the river water, adds the pollutants, namely, phenol and nitrogen, to it, and sends the water back to the river. The company has four possible ways to treat the water it uses before returning it to the river. The characteristics of each treatment are given in the following table:

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The Environmental Protection Agency (EPA) wants to restrict the amount of pollutants added by a company to the river water. The concentrations of phenol and nitrogen in the water are to be restricted to, respectively, P and N lbs. MG (million gallons) on a daily basis. The river has a flow of M MG/day. The company diverts a portion of the river water, adds the pollutants, namely, phenol and nitrogen, to it, and sends the water back to the river. The company has four possible ways to treat the water it uses before returning it to the river. The characteristics of each treatment are given in the following table:

(lbs. of pollutant)/MG after treatment

Treatment 1 2 3 4

Phenol, Nitrogen P1, N1 P2, N2 P3, N3 P4, N4

Cost/MG c1 c2 c3 c4

Assume: (i) that the river is initially free of pollutants; (ii) that addition of pollutants does not affect the amount of water flow; and (iii) that the company has to process at least K (MG/day) of river water. a) Set up a linear program to solve for the amount of water to be processed by each treatment, so that total cost of treatment is minimized. b) How does the formulation change if the EPA regulations apply not to total river concentration downstream from the plant, but rather to the concentration of effluent from the plant?