Regulatory agencies have imposed stream water quality criteria which require that the load...

Regulatory agencies have imposed stream water quality criteria which require that the load of a particular pollutant not exceed 0.00120 units per cubic meter (units/m3) of streamflow at any point in the river system. Five cities discharge wastewater into the river. Loads of the pollutant from sources other than the five cities is negligible. The cities cooperate to meet the water quality standards, with their goal being to min­imize the combined daily operating cost of all treatment plants. As the water flows down the stream, natural processes reduce the pollution level. The pollutant load is reduced by the following percentages (Pi,j) by natural processes between city i and city j as follows.

Treatment plant efficiency limits the percentage of the pollutant load that can be re­moved before discharging into the stream. For example, a maximum of 95 percent of the pollutant load generated by city 1 can be removed by the treatment plant at city 1. Pertinent data describing the system is as follows:

Use LP to determine the amount of pollutant that should be removed at the treat­ment plant at each city to minimize daily operating costs for the entire system while meeting the water quality criterion.