The campaign manager for a politician who is running for reelection to a politic

Question

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.

Explanation / Answer

a)

TV ads, radio ads, billboards, and newspaper ads.
Let w be number of TV ads, x be the number of radio ads, y be the number of billboard ads and z be the number of newspaper ads.

Minimize Cost = 900w + 500x + 600y + 180z
Below are the constraints,

Constraint 1: budget should not exceed 16000
900w + 500x + 600y + 180z <= 16000

Constraint 2: Number of people reached should be at least 15000000
40000w + 32000x + 34000y + 17000z >= 15000000

Constraint 3: Number of ads should not exceed particular value
w + x >= 6
w <= 10, x <= 10, y <= 10, z <= 10

Hence the LPP formulation will be

Min Z = 900w + 500x + 600y + 180z
subject to,
900w + 500x + 600y + 180z <= 16000
40000w + 32000x + 34000y + 17000z >= 15000000
w + x >= 6
w,x,y,z <= 10
w,x,y,z >= 0

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