The college director of global activities was hopeful that the print ads in the
ID: 453374 • Letter: T
Question
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
700
$25
200
$15
The communications director's market research revealed the following:
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. Twitter is complicated by the 140 character requirement. The communications director feels she needs five tweets to convey a single message about tours and semesters abroad, so for one message, the cost would be $25 for each of the five components of the single ad. Due to thumb fatigue, she feels that she has only 2800 characters left in her thumbs before the end of the semester. (A side note - During the intersession period, she plans to embark on a strict regimen of thumb yoga to prepare for the coming semester.)
Formulate the appropriate objective function and the LP problem for this scenario.
Medium
Exposure
Cost
Newspaper
5,000
$500
Radio
3,000
$250
700
$25
200
$15
Explanation / Answer
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