Horizon Wireless, a cellular telephone company, is expanding into a new city. Relay towers are necessary to provide wireless telephone coverage to the different areas of the city. A grid is superimposed on a map of the city to help determine where the towers should be located. The grid consists of 8 areas labeled A through H. Six possible tower locations (numbered L1–L6) have been identified, and each location could serve several areas. The table below indicates the areas served by each of the towers.Horizon wants to make sure that all areas of the city are served, while minimizing the number of towers that need to be built.

To determine the optimal tower locations for Horizon Wireless in the new city, we need to consider the areas served by each of the six identified locations (L1-L6) and ensure that all areas of the city are covered while minimizing the number of towers needed.

1. Start by examining the table that indicates the areas served by each tower location. This will help us understand the coverage provided by each location.

2. Look at the grid superimposed on the map of the city, with areas labeled A through H. This grid will help us visualize the different areas and their proximity to the tower locations.

3. Begin by identifying the areas that are not covered by any of the tower locations. These areas will need to be served by additional towers to ensure complete coverage.

4. Next, analyze the areas that are covered by multiple tower locations. Evaluate the proximity of these areas to each tower location and determine if any of the towers can be eliminated without compromising coverage.

5. Consider the efficiency of the tower locations in terms of minimizing the number of towers needed. Look for opportunities to consolidate coverage by selecting tower locations that serve multiple areas.

6. Continuously reassess the coverage and tower locations to find the most optimal solution. This may involve adjusting the placement of towers or considering additional tower locations if necessary.

7. Once a final set of tower locations is determined, ensure that they are strategically placed throughout the city to provide reliable coverage to all areas.

By following these steps, Horizon Wireless can expand into the new city with an efficient and effective wireless telephone coverage system, serving all areas while minimizing the number of towers needed.