A healthcare company plans to open its new chain of clinics in seven cities (1 to 7) within its earmarked budget. The population size (in thousands) in cities and associated investment budgets are tabulated below.

The company has earmarked 90 lakhs for the new investments. The company wants to open at most 5 clinics. No more than one city is selected between City 1 and City 3. If City 2 is included, then City 4 should be included. Determine the cities to be selected to maximize the reach to population.
a. Formulate an integer programming model for this problem.
b. Solve this model by using the computer.

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City 1 2 3 4 5 6 7 Population (in thousands) 45 55 66 40 35 48 56 Investment needed (in lakhs) 12 16 17 12 11 20 14