A mobile phone operator decides to equip a currently uncovered geographical zone. A budget is allocated to equip this region. 7 locations are possible for the construction of the transmitters. Every transmitter only covers a certain number of communities. For every community the number of inhabitants is known. Where should the transmitters be built to cover the largest population with the given budget?

Further explanation of this example: 'Applications of optimization with Xpress-MP', Section 12.6 'Location of GSM transmitters' (g6transmit.mos). Similar problems: Section 9.5 'Cutting of sheet metal' (d5cutsh.mos), Section 15.2 'CCTV surveillance' (j2bigbro.mos)

! Data file for `covering.mos'

COST: [1.8 1.3 4.0 3.5 3.8 2.6 2.1]

COVER: [(1  1) 1 (1  2) 1 (1  4) 1
        (2  2) 1 (2  3) 1 (2  5) 1
        (3  4) 1 (3  7) 1 (3  8) 1 (3 10) 1
        (4  5) 1 (4  6) 1 (4  8) 1 (4  9) 1
        (5  8) 1 (5  9) 1 (5 12) 1
        (6  7) 1 (6 10) 1 (6 11) 1 (6 12) 1 (6 15) 1
        (7 12) 1 (7 13) 1 (7 14) 1 (7 15) 1]

POP: [2 4 13 6 9 4 8 12 10 11 6 14 9 3 6]

BUDGET: 10

POST: [[26 26] [27 50] [54 23] [51 50] [66 40] [76 23] [87 44]]

POSC: [[18 19] [21 40] [24 61] [40 20] [43 44] [50 62] [64 16] [56 37] 
       [68 56] [64 27] [88 17] [75 36] [86 61] [96 52] [91 32]]