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Seven cities are being considered as potential locations for the construction ofat most four wastewater treatment plants. The following table provides the data for the situation. Missing links indicate that a pipeline cannot be constructed. Cost (S) of pipeline construction between citites per 1000 gal/hr capacity 1 2 3 4 5 6 7 From 100 200 50 2 120 150 3 400 120 90 120 120 5 200 100 200 6 110 180 70 7 200 150 Cost(Smillion) of 1.00 1.20 2.00 1.60 1.80 0.90 1.40 plant construction Population (1000s) 50 100 45 90 75 60 30 4 The capacity of a pipeline (in gallons per hour) is a direct function of the amount of wastewater generated, which is a function of the populations. Approximately 500 gallons per 1000 residents are discharged in the sewer system per hour. The maximum plant capacity is 100,000 gal/hr. Determine the optimal location and capacity of the plants