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Metro Telcom Systems develops, sells, and installs computer systems. The company has divided its customer base into five regions, and it has 15 representatives who sell and install the com- pany's systems. The company wants to allocate salespeople to regions so that they maximize daily sales revenue. However, whereas the sales increase as the number of salespeople allocated to a region increases, they do so at a declining rate, according to the following nonlinear formula:
total sales = a - ( b / x ) Following are the a and b parameters for daily sales in each region:
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Region
|
|
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1
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2
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3
|
4
|
5
|
|
a
|
$15,000
|
$24,000
|
$8,100
|
$12,000
|
$21,000
|
|
b
|
9,000
|
15,000
|
5,300
|
7,600
|
12,500
|
Because some of the regions are in urban areas and some are not, the representatives' daily expenses will differ among regions. The company has a daily expense budget of $6,500, and the daily expenses (including travel costs) per representative for each region average $355 for region 1, $540 for region 2, $290 for region 3, $275 for region 4, and $490 for region 5. Formulate and solve a nonlinear programming model for this problem to determine the number of representatives to allocate to each region to maximize daily sales.