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2. (Guret and Associates, 2002, Section 12.6) MobileCo is budgeting 15 million dollars to construct as many as 7 transmitters to cover as much population as possible in 15 con- tiguous geographical communities. The communities covered by each transmitter and the budgeted construction costs are given below. Transmitter Covered communities Cost (million $) 1 2. 3 4 5 6 7 1,2 2,3,5 1,7,9,10 4,6,8,9 6,7,9,11 5, 7, 10, 12, 14 12, 13, 14, 15 3.60 2.30 4.10 3.15 2.80 2.65 3.10 The following table provides the populations of the different comnunities: Community 1 2 3 4 S 6 7 8 9 10 11 12 13 14 15 Population in 2000s) 4 3 10 14 6 7 9 10 13 11 6 12 7 5 16 Which of the proposed transmitters should be constructed