The Westchester Company periodically sponsors public service

The Westchester Company periodically sponsors public service seminars and programs. Currently, promotional plans are under way for this year’s program. Advertising alternatives include television, radio, and newspaper. Audience estimates, costs, and maximum media usage limitations are as shown below:

To ensure a balanced use of advertising media, radio advertisements must not exceed 40% of the total             number of advertisements authorized. In addition, television should account for at least 20% of the total             number of advertisements authorized. The promotional budget is limited to $20,000. The company wishes to know how many commercial messages should be run on each medium to maximize total audience contact. Your job is to set up a linear program model for this problem. (Define your decision variable first)

Television RadioNewspaper Constraints Audience per advertisement 2 Cost per advertisement Maximum media usage 200,000 38,000 500 30 50,000 800 15 3,000 20

Solution

Budget $5,000 Total Number of ads 12 TV Radio Newspaper Audience reached       60,000       25,000       40,000 Cost per ad $400 $75 $250 Usage limit 10 20 10 Let number of ads per media x y z According to question x+y+z =< 12 x*400 + y*75 + z*250 =< $5,000 Objective function Maximize, P = x*6000+y*25000+z*40000