Metro Telcom Systems develops, sells, and installs computersystems. The company has divided its customer base into fiveregions, and it has 15 representatives who sell and install thecompany’s systems. The company wants to allocate salespeople toregions so that they maximize daily sales revenue. However, whereasthe sales increase as the number of increases, they do so at adeclining rate, according to the following nonlinear formula:
total sales = a - (b/x)
Following are the a and b parameters for daily sales in eachregion:
| | Region | | | |
| 1 | 2 | 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. Thecompany has a daily expense budget of $6,500, and the dailyexpenses (including travel costs) per representative for eachregion average $355 for region 1, $540 for region 2, $290 forregion 3, $275 for region 4, and $490 for region 5. Formulate andsolve a nonlinear programming model for this problem to determinethe number of representatives to allocate to each region tomaximize daily sales.
