Question

The campaign managers 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, Bill boards and Newspaper ads. The cost of these are; $900 for each Tv ad, $500 for each Radio ad, $600 for a bill board for 1 month and $180 for each Newspaper ad. The audience reached by each type of advertisement has been estimated to be $40,000 for each Tv ad, $32000 for each Radio ad, $34000 for each billboard and $17000 for each Newspaper ad. The total monthly advertisement budget is $16000 . The following goals have been establlished and ranked.

Goal 1:The number of people reached should be atleast 1,500,000.

Goal2: The total monthly advertisement budget should not be exceeded.

Goal3: Together, the number of ads on either Tv or Radio shoiuld be atleast 6.

Goal4: No more than 10 ads of any one type of adversetisement should be used.

Formulate this as a goal programming problem.

Answer 1

Step-1 Understand the problem

Step-2 Identify Objective function:- Maximise the audience reachability through these four types of advertisement strategies.

Max Audience Reach = 40000 TV ads + 32000 Radio ads +34000 Bill boards +17000 Newspaper ads

Step-3 Identify the constraints:-

Step - 4:- Solve the problem through Data Solver in excel by putting the limits and functions mentioned above:-

Note:- Billboard monthly budget is $600 irrespective of no of ads, so the equation for monthly budget changed slightly and became:-

900* TV ads + 500*Radio ads +600 (directly for Billboard) +180* Newspaper 16000

900* TV ads + 500*Radio ads +180* Newspaper 15400

Step-5 Optimal Solution

this Implies that the given objective cannot be fulfilled by the given above constraints.

Step-6 Advertising Plan