Ms. Osborne, marketing manager of the Midwest Typewriter Company, is trying to decide how to allocate her salespeople to the company's three primary markets. Market 1 is an urban area, and the salespeople can sell, on the average, 40 typewriters per week. The salespeople in the other two markets can sell, on the average, 36 and 25 typewriters per week, respectively.
For the coming week, three salespeople will be on vacation, leaving only 12 people available for duty. Also, because of a limited number of company cars, a maximum of 5 salespeople can be allocated to market I. The selling expenses per week for each salesperson in each area are: $80/week for market 1, $70/week for market 2, and $50/week for market 3. The budget for the next week is $750. The profit margin per typewriter is $15.
a. Formulate a linear programming model to determine how many salespeople should be assigned to each area next week to maximize profits.
b. Use the simplex method
c. Prepare the sensitivity report.