Guret and Associates (2002), Section 12.6. MobileCo is budgeting $15 million to construct as many as 7

Guéret and Associates (2002), Section 12.6. MobileCo is budgeting $15 million to construct as many as 7 transmitters to cover as much population as possible in 15 contiguous geographical communities. The communities covered by each transmitter and the budgeted construction costs are given below.

Transmitter Covered communities Cost (million $)

1 1, 2 3.60 2 2, 3, 5 2.30 3 1, 7, 9, 10 4.10 4 4, 6, 8, 9 3.15 5 6, 7, 9, 11 2.80 6 5, 7, 10, 12, 14 2.65 7 12, 13, 14, 15 3.10 The following table provides the populations of the different communities:

Community 1 2 3 4 5 6 7 8 9 10 Population (in 1000s) 10 15 28 30 40 30 20 15 60 12 Which of the proposed transmitters should be constructed?