Applied Mathematics is a way to use math to solve problems in the real world, like in economics, engineering, and medicine. 

My objective was to determine the optimal arrangement of cell phone transmission towers in Kern County to generate the best service coverage and the most profit using a mathematical model.

Can math find the best spots to build cell phone towers? This project uses a mathematical model to figure out where towers should go in Kern County. You assign each possible location a value based on population density and highway traffic.

Three different models come out of the math. One picks the most profitable spots with fewer towers. Another spreads towers out for the widest coverage. A third balances profit and coverage.

You also adjust for population growth to see how the best locations shift over time.

Project Title : Optimization of Cell Phone Service in Kern County

Objectives/Goals

My objective was to determine the optimal arrangement of cell phone transmission
towers in Kern County
to generate the best service coverage and the most profit using a mathematical
model.

Methods/Materials

I created a list of nodes that were representative of possible tower locations
and assigned each a
population density value, established points that corresponded to major highways
using linear equalities,
determined the total population and length of highway that was within the range
of each tower, assigned
an optimization value to represent the number of potential customers a tower
could support, and allotted
each highway node a value that represented the average traffic density for that
location (2004 project). For
my current project, based on the optimization value for a tower, a value was
produced to represent the
profits that could be generated by that tower#s customers. A representative cost
for maintenance that
increased with a potential tower#s distance from a city was also created. Using
these profit and cost
values, three models were generated: one representing the most profitable
arrangement of cell phone
towers; one representing the maximum service coverage to consumers without
causing the service
provider to lose money; and one that provided adequate coverage to consumers and
also generated profit
by using profit values of the first two models. The three models were
recalculated with different
population density values to represent population growth.

Results

The maximum profit models produced networks with relatively few towers
positioned in key locations
that would provide service to the most densely populated areas. The maximum
coverage models produced
networks that provided coverage to most population centers and major highways.
The balanced models
resembled the maximum service coverage models, but had fewer towers.

Conclusions/Discussion

The maximum profit model would be useful for a cell phone service provider that
does not have adequate
revenue to construct many towers. The maximum service coverage model would be
applicable to a
company unconcerned with current profits, but wanting to dominate the market.
The average service
provider would want to implement the balanced model because it produces profit
and also provides
enough service coverage to attract customers. All service providers would want
to use the data that
incorporate predicted population growth to sustain profitability.

Summary Statement

My project is a mathematical model that determines the arrangement of cell phone
transmission towers in
Kern County that is the most profitable and provides maximum service coverage.


Cell Tower Placement and Profit in Kern County

Optimization of Cell Phone Service

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Math is all about numbers, patterns, and solving problems. Computer science is about using math and technology to create computer programs and solve real-world problems. Together, they help us understand how things work, how to solve problems, and how to use technology to make our lives better!

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Cell Tower Placement and Profit in Kern County

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