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The Avalon Floor Cleaner Company is trying to determine the number of salespeople it should allocate to its three regions—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 as follows:
Because travel distances, costs of living, and other factors vary among the three regions, the annual cost of having a salesperson is $5,000 in the East, $11,000 in the Midwest, and $4,000 in the West. The company has $900,000 budgeted for expenses. To ensure nationwide exposure for its product, the company has decided 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.
Formulate an integer programming model for this problem.
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