The Avalon Floor Cleaner Company is trying to determine the number of salespeople it should allocate to its three regions mdash the East, the Midwest, and the west. The company has 100 salespeople that it wants to assign to the three regions. The annual average unit sales volume achieved by a salesperson in each region is 25,000 in the East, 18,000 in the Midwest and 31,000 in the West. Because travel distances, cost of living, and other factors vary among the three regions, the annual cost of having a salesperson is $6,000 in the East, $11,000 in the Midwest, and $7,000 the West. The company has $700,000 budgeted for expenses. To ensure nationwide exposure its product, the company has decide that each region must have at least 10 salespeople. The company wants to know how many salespeople to allocate to each region to maximize total average units sold.
1. Formulate a complete integer programming model for this problem
2. How many salespeople are assigned to the East?