The campaign manager for a politician who is running for reelection to a political office is planning the campaign. Four ways to advertise have been selected: TV ads, radio ads, billboards, and newspaper ads. The cost of these are $900 for each TV ad, $500 for each radio ad, $600 for a billboard for one month, and $180 for each newspaper ad. The audience reached by each type of advertising has been estimated to be 40,000 for each TV ad, 32,000 for each radio ad, 34,000 for each billboard, and 17,000 for each newspaper ad. The total monthly advertising budget is $16,000. The following goals have been established and ranked:
1. The number of people reached should be at least 1,500,000.
2. The total monthly advertising budget should not be exceeded.
3. Together, the number of ads on either TV or radio should be at least 6.
4. No more than 10 ads of any one type of advertising should be used.
(a) Formulate this as a goal programming problem.
(b) Solve this using computer software.
(c) Which goals are completely met and which of them are not?
Let T = number of TV ads, R = number of newspaper ads, B = number of billboard ads, and N = number of newspaper ads.
Minimize P1d1- + P2d2+ + P3d3- + P4d4+ + P4d5+ + P4d6+ + P4d7+
This solution provides advice to the campaign manager to set up an advertising campaign by using the number of people reached, budget, number or TV or radio ads and the restriction on number of each individual types of ads. It also evaluates the goal programming problem and looks at which goals are met and which are not.