KPS Communications is planning to bring wireless Internet access to the town of Ames, Iowa. Using a geographic information system, KPS has divided Ames into the following 5 by 5 grid. The values in each block of the grid indicate the expected annual revenue (in $1,000s) KPS will receive if wireless Internet service is provided to the geographic area represented by each block.

 

KPS can build wireless towers in any block in the grid at a cost of $150,000 per tower. Each tower can provide wireless service to the block it is in and to all adjacent blocks. (Blocks are considered to be adjacent if they share a side. Blocks touching only at corner point are not considered adjacent.) KPS wants to determine how many towers to build and where to build them in order to maximize profits in the first year of operations. (Note: If a block can receive wireless service from two different towers, the revenue for that block should only be counted once.)

a. Create a spreadsheet model for this problem and solve it.

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b. What is the optimal solution, and how much money will KPS make in the first year?

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c. In order to be the dominant player in this market, KPS is also considering providing wireless access to all of Ames—even if it is less profitable to do so in the short term. Modify your model as necessary to determine the tower location plan that maximizes the wireless coverage in Ames. What is the optimal solution, and how much profit will it provide?

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d. Clearly, there is a trade-off between the objective in par b of maximizing profit and the objective in part c of maximizing wireless coverage. Determine the solution that minimizes the maximum percentage deviation from the optimal objective function values from parts b and c.

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e. Suppose KPS considers maximizing profit to be twice as important as maximizing coverage. What solution does this suggest?

Expected Annual Revenue by Area (in $1,000s) $34 $43 $62 $42 $34 $64 $43 $71 $48 $65 $57 $57 $51 $61 $30 $32 $38 $70 $56 $40 $68 $73 $30 $56 $44