A telecom company needs to build a set of cell towers to provide signal coverage for the inhabitants of a given city. A number of potential locations  where the towers could be built have been identified. The towers have a fixed range, and due to budget constraints only a limited number of them can be built. Given these restrictions, the company wishes to provide coverage to the largest percentage of the population possible. To simplify the problem, the company has split the area it wishes to cover into a set of regions, each of which has a known population. The goal  is then to choose which of the potential regions the company should build cell towers on in order to provide coverage to as many people as possible.

The table below shows which of the regions are covered when a tower is build in that region. Note "-" means the tower  build cannot serve the region. 

	Region 0	Region 1	Region 2	Region 3	Region 4	Region 5
Region 0	1	1	-	-	-	1
Region 1	1	1	-	-	-	-
Region 2	-	-	1	1	-	-
Region 3	-	-	1	1	-	1
Region 4	-	-	-	-	1	-
Region 5	1	-	-	1	-	1

The population at each region is stated in the following table.

	Region 0	Region 1	Region 2	Region 3	Region 4	Region 5
Population	523	690	420	1010	1200	850

The cost to build a cell tower at each location site is stated in the following table.

	Cost (millions of USD)
Region 0	4.2
Region 1	6.1
Region 2	5.2
Region 3	5.5
Region 4	4.8
Region 5	9.2

The allocated budget is $20,000,000

Hint: The objective is to maximize the population covered. 

Hint 2: Model this problem as a set-covering problem. An additional constraint on the budget needs to be added to the model. 

Difficulty Level: Easy 

Answer rating: 100% (QA)

This problem can be modeled as a setcovering problem with an additional budget constraint The goal is to choose a subset of regions to build cell towe... View the full answer