Horizon Wireless, a cellular telephone company, is expanding into a new area. Re
ID: 3319109 • Letter: H
Question
Horizon Wireless, a cellular telephone company, is expanding into a new area. Relay towers are necessary to provide wireless telephone coverage to the different areas of the county. A grid superimposed on a map of the county shows that the county can be divided into 8 areas, labeled A-H. There are six possible tower locations. The table below indicates the areas served by each of the towers. 8. Tower Areas Location Covered 1 A,BD 2 B.C.G 3 C,D,EF 4 E.F.H 5 E,G,H A,D,F a. Formulate this as a binary linear programming model to minimize the number of towers required to cover all the areas. Write your LP in the space below Use the template in Excel to solve your LP. Write the optimal tower locations belowExplanation / Answer
The boxes in green, are decision variables
The boxes in blue are constrains
The boxes in orange is the objective function
The formulae used:
Tower/Area Decision Variable A B C D E F G H
1 1 =B2 =B2 =B2
2 1 =B3 =B3 =B3
3 0 =B4 =B4 =B4 =B4
4 1 =B5 =B5 =B5
5 0 =B6 =B6 =B6
6 0 =B7 =B7 =B7
No of towers =SUM(B2:B7) =SUM(C2:C7) =SUM(D2:D7) =SUM(E2:E7) =SUM(F2:F7) =SUM(G2:G7) =SUM(H2:H7) =SUM(I2:I7) =SUM(J2:J7)
Obj Fun Minimize >= >= >= >= >= >= >= >=
1 1 1 1 1 1 1 1
All areas covered
The solution is:
Tower/Area Decision Variable A B C D E F G H
1 1 1 1 1
2 1 1 1 1
3 0 0 0 0 0
4 1 1 1 1
5 0 0 0 0
6 0 0 0 0
No of towers 3 1 2 1 1 1 1 1 1
Obj Fun Minimize >= >= >= >= >= >= >= >=
1 1 1 1 1 1 1 1
All areas covered
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