Linear Model Help

[Juggler]

I was just wondering how to develop a model on the following question.

An ad campaign for a new snack chip will be conducted in a limited geographical area and can use TV time, radio time, and newspaper ads. Information about each medium is shown below.


Medium Cost Per Ad # Reached Exposure Quality
TV 500 10000 30
Radio 200 3000 40
Newspaper 400 5000 25

If the number of TV ads cannot exceed the number of radio ads by more than 4, and if the advertising budget is $10000, develop the model that will maximize the number reached and achieve an exposure quality of at least 1000.

[HallsofIvy]

Originally Posted by Juggler

I was just wondering how to develop a model on the following question.

An ad campaign for a new snack chip will be conducted in a limited geographical area and can use TV time, radio time, and newspaper ads. Information about each medium is shown below.


Medium Cost Per Ad # Reached Exposure Quality
TV 500 10000 30
Radio 200 3000 40
Newspaper 400 5000 25

If the number of TV ads cannot exceed the number of radio ads by more than 4, and if the advertising budget is $10000, develop the model that will maximize the number reached and achieve an exposure quality of at least 1000.

I'm having trouble understanding your information. I take it that there are 3 kinds of media- TV cost $500 per ad and will reach 10000 people, Radio cost $200 per ad and will reach 3000 people, and the newspaper cost $400 per ad and will reach 5000 people but what is "Exposure quality"? How is it measured? Is the total "exposure quality" for a medium the number of ads times the "exposure quality" for that medium?

First "name things". Let T= number of TV ads, R= number of radio ads, and N= number of newspaper ads.

" the number of TV ads cannot exceed the number of radio ads by more than 4" Okay, T<= R+ 4.

"the advertising budget is $10000". T "TV ads" at $500 each cost 500T dollars. R "radio ads" at $200 each cost 200R dollars. N "newspaper ads" at $400 per ad cost 400N dollars. The total cost is 500T+ 200R+ 400N and that cannot be more than $10000. Okay 500T+ 200R+ 400N<= 10000.
If my guess that the total exposure quality is the "exposure quality" for ech medium is the exposure quality for that medium time the number of adds is correct, then "achieve an exposure quality of at least 1000" becomes 30T+ 40R+ 25N>= 1000.

The "object function", number reached, is 10000T+ 300R+ 400N.

[Juggler]

Yeah, there are three types of media. Thanks for the help on naming the variables. Its kind of hard to understand, so here is the problem word for word (attachment).

I couldn't understand the " the number of TV ads cannot exceed the number of radio ads by more than 4". It makes sense now. Thanks again for the help.

[HallsofIvy]

It is still not clear what "exposure quality" but if my guess that the total "exposure quality" is the sum of the "exposure quality" for each medium times the number of adds for that medium, then the inequalities, and object function I gave before are correct.