Problem
A company is trying to determine how to allocate its $145,000 advertising budget for a new product. The company is considering newspaper ads and television commercials as its primary means for advertising. The following table summarizes the costs of advertising in these different media and the number of new customers reached by increasing amounts of advertising.
Media & No of Ads No of New Customers Reached Cost per Ad
Newspaper: 1-10 900 $1,000
Newspaper: 11-20 700 $900
Newspaper: 21-30 400 $800
Television: 1-5 10,000 $12,000
Television: 6-10 7,500 $10,000
Television: 11-15 5,000 $8,000
For instance, each of the first 10 ads the company place in newspapers will cost $1000 and is expected to reach 900 new customers. Each of the next 10 newspaper ads will cost $900 and is expected to reach 700 new customers. Note that the number of new customers reached by increasing amount of advertising decreases as the advertising saturates the market. Assume the company will purchase no more than 30 newspaper ads and no more than 15 television ads.
Formulate an LP model for this problem to maximize the number of new customers reached by advertising.