MobileCo is budgeting 15$ millions to construct as many as 6 transmitters to cover as much population as possible in 10 contiguous geographical communities. The communities covered by each transmitter and the budgeted construction costs are listed in Table 1. The populations of different communities in provided in Table 2.

(a). (30 points) Formulate an integer programming telling which of the proposed transmitter should be constructed in order to maximize the population coverage.

(b). (10 points) Write a Matlab script to solve the formulation in (a) using intlinprog.

Cost (lion S) 3.60 2.30 4.10 3.15 2.80 2.65 Transmitter red Communities 2,3,5 1,7,9,10 4,6,8,9 6,7,9 5,7,10 6 Table 1: Costs and coverage table, Problem 2 Community 1 23 4 5 6 789 10 Population in 1000s 10 15 28 30 40 30 20 15 60 12 Table 2: Populations of the different communities, Problem 2 Cost (lion S) 3.60 2.30 4.10 3.15 2.80 2.65 Transmitter red Communities 2,3,5 1,7,9,10 4,6,8,9 6,7,9 5,7,10 6 Table 1: Costs and coverage table, Problem 2 Community 1 23 4 5 6 789 10 Population in 1000s 10 15 28 30 40 30 20 15 60 12 Table 2: Populations of the different communities, Problem 2