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Question 1143181: website ads Nielson's net ratings for the month of December 2002
indicated that in United States , AOL had a unique audience of
about 76.4 million people and Yahoo! had a unique audience of
about 66.2 million people . An advertising company wants to
purchase website ads to promote a new product. Suppose that the
monthly cost of an ad on the AOL website is $ 1200 and the monthly
cost of an ad on the Yahoo! website is $1100. Determine how many
months an ad should run on each website to maximize the number of
people who would be exposed to it. Assume that , for future months,
the monthly website audience remains the same as given for
December 2002. Also assume that the advertising budget is $35,000
and that is has been decided to advertise on Yahoo! for at least ten
months.
Answer by ikleyn(52805)   (Show Source):
You can put this solution on YOUR website! .
The problem is to maximize the total number of exposing ads-persons
P(X,Y) = 76.4X + 66.2Y millions of ads-persons (OBJECTIVE FUNCTION)
under this restrictions
1200X + 1100Y <= 35000,
X >= 0, Y >= 10,
where X and Y are the number of months for the ad at AOL and Yahoo, respectively.
It is standard simple geometric 2D linear minimax problem to be solved by the Linear Programming method.
So, draw the feasible area - in this case it is a quadrilateral at QI;
find the coordinates of the corners;
calculate the objective function at the corners, and
determine at which corner the objective function has a maximum.
This point (this corner) will be the solution point to the problem.
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See the lesson
- Solving minimax problems by the Linear Programming method
at his site. Find there many similar solved problems, that are your TEMPLATES.
See also this list of links
https://www.algebra.com/algebra/homework/Inequalities/Inequalities.faq.question.1142000.html
https://www.algebra.com/algebra/homework/Sequences-and-series/Sequences-and-series.faq.question.1137172.html
https://www.algebra.com/algebra/homework/Graphs/Graphs.faq.question.1136382.html
https://www.algebra.com/algebra/homework/Coordinate-system/Coordinate-system.faq.question.1134444.html
https://www.algebra.com/algebra/homework/Graphs/Graphs.faq.question.1131906.html
https://www.algebra.com/algebra/homework/coordinate/word/Linear_Equations_And_Systems_Word_Problems.faq.question.1131043.html
https://www.algebra.com/algebra/homework/word/finance/Money_Word_Problems.faq.question.1129285.html
https://www.algebra.com/algebra/homework/Finance/Finance.faq.question.1128383.html (*!*)
https://www.algebra.com/algebra/homework/Linear-equations/Linear-equations.faq.question.1123217.html (!)
https://www.algebra.com/algebra/homework/playground/test.faq.question.1112482.html
https://www.algebra.com/algebra/homework/Finance/Finance.faq.question.1102103.html
to similar solved problems in the archive of this forum.
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I assume that this problem is for 10-th or 11-th grade school student or a College student.
At this stage, the student do not need to be a spoon-feeded.
Having a good sample, he (or she) can do the rest on his (or her) own.
Good samples are just provided and the setup is just done.
Try to do the rest on your own.
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