A cellular telephone company is expanding into a new era. 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
A cellular telephone company is expanding into a new era. 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 1 to 6) have been identified, and each location could serve several areas. The company would like to minimize the number of towers required to cover all the areas. The table below shows which areas are covered by each tower location.
|
Tower Locations |
1 |
2 |
3 |
4 |
5 |
6 |
|
Areas Covered |
A, B, D |
B, C, G |
C, D, E, F |
E, F, H |
E, G, H |
A, D, F |
Formulate and solve the binary programming model using Excel. Determine the following:
a) Optimal number of towers needed to cover all areas.
b) How many set covering constraints are in the model?
c) In optimal solution, which tower locations are selected?
d) In optimal solution, which tower location covers Area D?
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