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 company€™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:

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 dailysales.

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Region 2 4 5 a $15,000 $24,000 $8,100 $12,000 $%21,000 12,500 9,000 15,000 5,300 7,600