PHYSICS CS165
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# LLILIJ l-IHl'ul-III'IU'IU'I'HIHID As the head of anaiytics for a cell phone company, you have been asked to optimize the location of cell towers in a...

This is a maximum coverage problem with integer and binary programming. I have these so far:

Variables

Rj (1 if region is covered, 0 if not)

Ti (1 if tower is built, 0 if not)

Pi (1 if it has a neighborhood, 0 if not)

The objective function must be maximiza sum(pi*rj)

And I have only one restriction so far:

sum(ti*pi)<=70%

LLILIJ l-IHl'ul-III'IU'IU'I‘HIHID As the head of anaiytics for a cell phone company, you have been asked to
optimize the location of cell towers in a new area where your company wants to
provide service. The new area is made up of several neighborhoods. Each
neighborhood is represented by a black house icon in the accompanying image. it cell tower can be placed on any square {including squares with or without a
neighborhood}. Once placed, a cell tower provides service to 9 squares {the 8
adjacent squares surrounding it and the 1 it sin on}. For example, if you placed a
cell tower in I32, it would provide service to A1, El, (31, A2, BE, C2, A3, BB, and C3. The company recognizes that it may not be worthwhile to cover all neighborhoods,
so it has instructed you that it needs to cover only &quot;IDES of the neighborhoods in
the new area. Each cell tower is expensive to construct and maintain so it is in
your best interest to only use the minimum number of cell towers. Question: What is the minimum number of cell towers needed to provide
service to at least THEE of the neighborhoods?

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