Josh Steele manages a professional choir in a major city. His marketing plan is focused on generating additional local demand for concerts and increasing ticket revenue and also gaining attention at the national level to build awareness of the ensemble across the country. He has $20,000 to spend on media advertising. The goal of the advertising campaign is to generate as much local recognition as possible while reaching at least 4,000 units of national exposure. He has set a limit of 100 total ads.

Additional information is shown next.

Local Exposure National Exposure Limit FM radio spot $80.00 110 40 30 AM radio spot $65.00 55 20 30 Cityscape ad $250.00 80 5 24 MetroWeekly ad $225.00 65 8 24 Hometown paper ad $500.00 400 70 10 Neighborhood paper ad $300.00 220 40 10 Downtown magazine ad $55.00 35 0 15 Choir journal ad $350.00 10 75 12 Professional organization magazine ad $300.00 20 65 12 The last column sets limits on the number of ads to ensure that the advertising markets do not become saturated.

a. Find the optimal number of ads of each type to run to meet the choir’s goals by developing and solving an integer optimization model.

b. What if he decides to use no more than six different types of ads? Modify the model in part

(a) to answer this question.