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# Linear Programming - Max Cover

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Linear Programming - Max Cover
DixieNet is an Internet service provider for residential customers in a southern state. The company is small now but plans to expand. Its first major goal is to establish a set of hubs throughout the state so that all residents of the state can access a hub via a local phone call. Local phone service is available between all pairs of adjacent counties in the state. Thus, if there is a hub in a given county, or in one of the adjacent counties, then residents of that county have the desired access.
County adjacencies are shown below. Values of 1 indicate counties that are adjacent to each other and values of 0 show counties that are not adjacent to each other. Each county is considered to be adjacent to itself.

Questions: Please use excel solver and also provide a "concise" algebraic formulation / narration)

a) Solve the Max Cover model for DixieNet with 1, 2 and 3 hubs.
b) DixieNet has decided to use sales representatives to generate sales at the grass roots level. Each sales rep will be assigned a primary county and a secondary county. The sales rep then travels within these 2 counties only. That way, once a sales rep is assigned a particular primary and secondary country, those populations are covered.
b) i) Assuming that you initially had 1 sales rep, which county would you assign him to (primary and secondary) in order to maximize population coverage? Develop a Greedy Heuristic for solving this.
b) ii) Suppose you had 2, 3, 4, or 5 sales reps. How would you assign them? Develop a Greedy Heuristic for solving this and also, the most concise Integer programming model to solve the problem optimally. Show the algebraic formulation and implement and solve it in excel.
Note: For both parts a. and b. above, display your solutions in a neat tabular format for each case considering that you don't have a map on which to show them

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** Please see attached files for the complete solution response **

Linear Programming - Max Cover
DixieNet is an Internet service provider for residential customers in a southern state. The company is small now but plans to expand. Its first major goal is to establish a set of hubs throughout the state so that all residents of the state can access a hub via a local phone call. Local phone service is available between all pairs of adjacent counties in the state. Thus, if there is a hub in a given county, or in one of the adjacent counties, then residents of that county have the desired access.
County adjacencies are shown below. Values of 1 indicate counties that are adjacent to each other and values of 0 show counties that are not adjacent to each other. Each county is considered to be adjacent to itself.
1 2 3 4 5 6 7 8 9 10 11 12 13 14
1 1 1 0 0 1 0 0 0 0 0 0 0 0 0
2 1 1 1 0 1 0 0 0 0 0 0 0 0 0
3 0 1 1 1 1 1 0 0 0 0 0 0 0 0
4 0 0 1 1 0 1 0 1 0 0 0 0 0 0
5 1 1 1 0 1 1 0 0 1 1 0 0 0 0
6 0 0 1 1 1 1 1 0 0 1 1 0 0 0
7 0 0 0 0 0 1 1 1 0 0 1 1 0 0
8 0 0 0 1 0 0 1 1 0 0 0 1 0 0
9 0 0 0 0 1 0 0 0 1 1 0 0 1 0
10 0 0 0 0 1 1 0 0 1 1 1 0 1 0
11 0 0 0 0 0 1 1 0 0 1 1 1 1 0
12 0 0 0 0 0 0 1 1 0 0 1 1 1 1
13 0 0 0 0 0 0 0 0 1 1 1 1 1 1
14 0 0 0 0 0 0 0 0 0 0 0 1 1 1

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#### Solution Summary

This solution explains how to solve the given linear programming questions max cover.

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