In Problem 23, the shortages should be met by supplying from groundwater resources. The cost of meeting the demand by supplying from groundwater is a function of the volume of water that should be extracted. The cost of water extraction for domestic demands is estimated as C_Dom = 1000 . x²  _Dom  , where x_dom is the volume of water extracted for domestic uses.

The cost of water extraction for irrigation purposes is estimated as C_irr = 250 . x²_irr

, where x_irr

is the volume of water extracted for irrigation.

• Formulate the problem for finding the optimal monthly volumes of water allocation.

• 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 The cost of water supply from surface water is about 0. 1$/L, where the cost of water withdrawn from groundwater is three times the surface water.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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TABLE 6.15 Considered Water Demand Management Strategies in the City of Problem 23 Maximum Reduction Cost (S) Per Each Liter Reduction in Consumption Demand Management Strategy Training programs Leakage reduction Using of water consumption reduction strategies Use of recycled water for landscaping/parks irrigation in Consumption 2% 0.02 8% 0.5 1.5% 0.6 6% 0.2