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) that KPS will receive if it provides wireless Internet service to the geographic area represented by each block.
|
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
|
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 points are not considered adjacent.) KPS would like to determine how many towers to build and where to build them to maximize profits in the first year of operations. (If a block can receive wireless service from two different towers, the revenue for that block should be counted only once.)
a. Create a spreadsheet model for this problem and solve it.
b. What is the optimal solution and how much money will KPS make in the first year?
c. Suppose KPS is required to provide wireless service to all of the blocks. What is the optimal solution and how much money will KPS make in the first year?