In Problem 23, the city discharges its wastewater to the river upstream of the agricultural lands. The

Question:

In Problem 23, the city discharges its wastewater to the river upstream of the agricultural lands. The monthly wastewater discharge rate is about 20% of the water use of the city in each month. In order to keep the quality of the river flow in an acceptable range for irrigation, the pollution load of the city wastewater should be reduced by primary treatment, which has an additional cost equal to $12,000 per million cubic meters.

• Formulate the problem for optimizing the water allocation from this river.

• Solve the problem using linear programming.

Data from problem 23 Consider a small city with a population of 100,000. The water consumption per capita in this city is about 250 L/day. The available water supply system of this city includes a surface reservoir with an annual water supply capacity of 15 MCM. The population growth rate has been determined equal to 2% and the migration rate is about 0. 5%. In the current rate of water consumption per capita will increase 1% each year. There is also an aquifer near the city with a water supply capacity of 5 MCM/year. The treatment plant of this city has limitation on the TDS intake of 300 mg/L. The TDS of surface water and groundwater is 250 and 400 mg/L, respectively. The cost of water supply from surface water is about 0. 1$/L, where the cost of water withdrawn from groundwater is three times the surface water. The water supply manager of the city has planned some demand management studies with estimated reduction in water consumption and cost as given in Table 6. 15. Develop an optimization model for water supply development and demand management schemes in this city for the next 50 years. The objective of the optimization model is to minimize the water deficit and water supply cost. The rate of return on investments is considered equal to 5%. Make any other assumption needed to solve this problem.

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