SOLVE BY HAND-NO EXCEL- SHOW FULL SOLUTION

Seven cities are being considered as potential locations for the construction of at 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 To 1 2 3 4 5 6 7 From 1 100 200 50 2 120 150 3 400 120 90 4 120 120 5 200 100 200 6 110 180 70 7 200 150 Cost(S million) 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 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