Water Resources Problem Linear Programming Water Resources Problem

Example1 Objective function Subject to

2: Water Resources Problem The total water demand for Gaza Strip is 160 MCM/yr (80 for Municipal and Industrial and 80 for agriculture). The M&I demand should be satisfied from groundwater wells, brackish water desalination (70% efficiency), and central seawater desalination. The agricultural demand should be satisfied from groundwater wells and from the treated wastewater (TWW) but at least 25% of the agricultural demand should come from the groundwater wells. The maximum capacity of the central seawater desalination plant is 60 MCM/yr. The Palestinian water quality standards require that the water supplied to the M&I should have TDS concentration less than 600 mg/l and the water supplied to agriculture should have TDS concentration of less than 1100 mg/l. The integrated aquifer management plan recommended that the max groundwater abstraction should be 100 MCM/yr. The following table shows the estimated benefits, production cost, and the produced quality of each source.

Source Benefit Cost Quality $/m3 TDS (mg/l) Sea water desalination 0.5 0.45 500 Brackish water desalination 0.3 Wells for M&I 0.4 0.15 1200 Wells for agriculture 0.25 TWW for agriculture 0.2 600 TWW for aquifer 0.1 Design a Linear Programming model to seek the optimal utilization from each source? Explain the binding and the slack conditions shown in the answer report? What is the minimum amount of seawater desalination to keep the solution feasible?