Question

Atwitter The college director of global activities was hopeful that the print ads in the school newspaper and 30 second spots on the campus radio station would spur some interest in the array of study tour and study abroad options he had secured. The communications director for the college had other ideas; she favored a social media campaign consisting of tweets and Facebook postings. "This is the most ridiculous thing I ever heard of," he whined to the dean. The communications director's market research revealed the following: Medium Exposure Cost Newspaper 5,000 $500 Radio 3,000 $250 Twitter 700 $25 Facebook 200 $15 The advertising budget is $3500, but there is no requirement that all the money be spent. The newspaper has only four issues before the end of the semester, but the radio is a 24/7 operation and has two dozen 30 second slots available. Facebook postings must be alternated with the rest of the mindless drivel posted on the college page; thus there is space for only three postings before the end of the semester.

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Let the media be classified as below - No. of Newspaper ads-N; No. of Radio ads-R; No. of Facebook post ads - F; No. of Twitter posts - T a. Formulation of LP: The objective function here is to maximize exposure to the audience Z = 5000N+3000R+700T+200F subject to constraints - 500N+250R+25T+15F<=3500 -----> Budget Constraint - ->1 N<=4 ----> Newspaper Constraint --->2 R<=24 -> Radio ad Constraint ->3 F<=3 ----> Facebook posts ---->4 For number of tweets, we have 2800 characters as the maximum the director can type. Each twitter msg has 140 characters----> this implies maximum number of tweets = 2800/140 = 20 tweets. But 5 tweets will become a single ad according to the information provided---> this implies for 20 tweets, it will be 20/5 = 4 twitter posts/ads. Hence, twitter constraint is T<=4 ---> Twitter Constraint --->5 N,R,F,T >=0