A municipal water district supplies water to three cities from the following three sources...

A municipal water district supplies water to three cities from the following three sources. Source A is a well with relatively low pumping cost in an aquifer with relatively high salinity. Source B is a well with higher pumping cost in an aquifer with better quality water. Source C is a reservoir on a river with good quality (low salinity) and no pumping cost. Each of the three cities may be supplied from combinations of the three sources. The unit cost per m3 for pumping water from each source to each city is tabulated below. The daily water demand for each city is shown in the last row of the table.

The total dissolved solids (TDS) concentration in grams per cubic meter (g/m3) for each? source is shown below. The amount of water available from each source (capacity) is also tabulated.

The TDS concentration of the municipal water supply cannot exceed 500 g/m3. Water from alternative sources can be blended to achieve this water quality standard. Source C is a multiple-purpose reservoir from which water can be withdrawn for municipal water supply only if the water demands and quality standards cannot be met in any other way. Water supply diversions adversely affect hydropower, recre­ation, and other reservoir purposes. The amount of water supplied from source C must be minimized, subject to meeting water supply demands and the 500 g/m3 max­imum allowable TDS limit. Formulate and solve an LP model to determine the amount of water supplied from each source for each city that minimizes pumping costs while meeting water demands and water quality standards.