(Solved): A map presented below illustrates the 11 regions of a city. This city plans to minimize the number o ...

A map presented below illustrates the 11 regions of a city. This city plans to minimize the number of its fire emergency stations. If the city decides to locate a fire station in a region, that station can serve the host region as well as the neighboring regions. For instance, if a station is placed in region 1, it can serve regions 1,2,3, and 4. So, the following constraint should be considered: ???????? + ???????? + ???????? + ???????? ? 1

Find the minimum number of stations for this city such that all the regions will be served.

Figure 1, shows the map of a city with 11 regions. Neighboring regions have at least one common edge (border). For instance, region 11 has two neighbors, regions 9 and 10.

A map presented below illustrates the 11 regions of a city. This city plans to minimize the number of its fire emergency stations. If the city decides to locate a fire station in a region, that station can serve the host region as well as the neighboring regions. For instance, if a station is placed in region 1 , it can serve regions \( 1,2,3 \), and 4 . So, the following constraint should be considered: \[ x_{1}+x_{2}+x_{3}+x_{4} \geq 1 \] Find the minimum number of stations for this city such that all the regions will be served. Figure 1 , shows the map of a city with 11 regions. Neighboring regions have at least one common edge (border). For instance, region 11 has two neighbors, region 9 and \( 10 . \)