Suppose that the distances between fifteen cities are as in the table below, An airline wishes to institute service among these cities. Assuming that flight cost is directly proportional to distance, find an optimal routing system that provides service to all cities.

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City 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1 24 20 22 15 60 20 24 31 34 36 27 28 29 34 32 45 12 21 14 50 41 34 40 18 20 25 37 14 20 35 80 46 35 28 49 38 57 35 41 11 234567890122 14 31 18 20 26 40 35 72 26 47 22 36 46 19 30 46 38 35 27 21 50 43 20 40 34 58 25 32 18 33 60 35 31 27 36 22 47 61 35 25 17 32 43 71 54 43 25 30 32 40 45 21 15 26 29 33 36 27 29 31 40 24 16 19 31 26 23