A candidate for the next presidential election is trying to determine how to all
ID: 466014 • Letter: A
Question
A candidate for the next presidential election is trying to determine how to allocate their $250,000 advertising budget. The candidate is considering Facebook ads and television commercials as the primary means for advertising. Each Facebook ad costs $100 and is expected to reach 10,000 people. Each television commercial costs $1000 and is expected to reach 27,000 people. Assume that the candidate will purchase no more than 500 Facebook ads and no less than 150 television ads.
Write the linear programming formulation to help the candidate determine how many Facebook ads and how many television commercials they should purchase in order to maximize the people reached.
Explanation / Answer
Decision variables :
X1 = TOTAL NO OF ADS TO FACEBOOK
X2 = TOTAL NO OF ADS TO TELIEVISION COMMERCIALS
Objective function :
MAX Z = 10,000 X1 + 27,000 X2 ( Maximize the people reached)
Constraints:
100 X1 + 1000 X2 <= 2,50,000 ( advertising budget)
X1<= 500 ( purchase no more than 500 Facebook ads)
X2 >=150 (no less than 150 television ads)
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