5. The campaign manager for a politician who is running for reelection to a poli

Question

5. 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.

Formulate this as a goal programming problem. with justifications

Explanation / Answer

There are 4 decision variables in the problems.

Let us consider that x1, x2,x3 and x4 represents the advertising units which are to be TV ads, radio ads, billboards, and newspaper ads.

The main objective of this problem is to maximize the total number to viewers

Maximize Z =(40,000 x1 + 32000 x2 + 34000 x3 + 17000 x4) or,

Maximize Z =(4 x1 + 3.2 x2 + 3.4 x3 + 1.7 x4)

Constraints are as below:-

Number of people reached:-

(40,000 x1 + 32,000 x2 + 34,000 x3 + 17,000 x4) 1,500,000

Advertising budget:- 900 x1 + 500 x2 + 600 x3 + 180 x4 16,000

6 x1 + 7.5 x2 + 3 x3 + 1.5 x4 80

Number of ads:- x1+x2 6

x1 10

x2 10

x3 10

x4 10

x1, x2,x3,x4 0

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