Introduction to Management Science 12th Edition by Bernard Taylor

Exercise 16

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 daily sales.