Linear Model Help - Physics Forums: Physics, Astronomy, Math, & Philosophy Forums!

 Physics Forums: Physics, Astronomy, Math, & Philosophy Forums! Linear Model Help
 Register FAQ Members List Calendar Search Today's Posts Mark Forums Read
#1
11-25-2007, 09:37 AM
 Juggler Junior Member Join Date: Nov 2007 Posts: 2
Linear Model Help

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
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.
#2
12-04-2007, 02:41 PM
 HallsofIvy Senior Member Join Date: Oct 2006 Posts: 464

Quote:
 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?

" 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.
#3
12-05-2007, 08:21 AM
 Juggler Junior Member Join Date: Nov 2007 Posts: 2

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.
Attached Images

#4
12-06-2007, 02:10 PM
 HallsofIvy Senior Member Join Date: Oct 2006 Posts: 464

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.

 Thread Tools Display Modes Linear Mode

 Posting Rules You may not post new threads You may not post replies You may not post attachments You may not edit your posts vB code is On Smilies are On [IMG] code is On HTML code is Off
 Forum Jump User Control Panel Private Messages Subscriptions Who's Online Search Forums Forums Home Physics Forums Dr. Elliot McGucken's Announcements Physics & Math in Video Games Rebel Scientists : A Renaissance in Physics Physics, Philosophy, and Math General Physics General Philosophy General Math General Physics, Math, & Philosophy Homework Physics Classical Physics Quantum Physics Condensed Matter / Solid State Physics Special & General Relativity String Theory, LQG, Branes Nuclear & Particle Physics Experimental Physics Techniques Physics Fraud: Physics Crackpots: Physics Hoaxes Cutting Edge Physics Research Pulsoid Theory Physics Pub: Brain Teasers/Puzzles/Paradoxes Time Vector / Relativity / Moving Dimensions     Time Vector Theory (http://members.triton.net/daveb)     Moving Dimensions Theory     Reality Physics (www.realityphysics.com)     Structured Time Theories Astronomy & Astrophysics Astronomy & Cosmology Stellar Astrophysics: Stars, The Sun The Planets, Planetary Motion, Newton, Kepler Large Scale Structure of The Universe Mathematics General Math Calculus Differential Equations Linear Algebra, Advanced Algebra Differential Geometry & Topology Probability, Statistsics Set Theories, Infinities, Number Theory Engineering & Applied Science Architectural Engineering Automotive Engineering, NASCAR Mechanical Engineering Electrical Engineering Materials & Chemical Engineering Systems, Design, and Industrial Engineering Technology / Information Technology Computers Internet & Information Technologies Search & Indexing Technologies Philosophy General Philosophy Metaphysics and Epistemology Ethics, Morality, Moral Theories, Religion Logic Philosophy of Religion Philosophy of Language * Linguistics Philosophy of Politics & Law Human Philosophy: Anthropology, Sociology and Psychology Philosophy of the Arts Famous Books & Famous Physicists The Written Word Books & Literature Science & Religion Poetry for Physicists Famous Books & Famous Physicists Relativity: The Special and the General Theory by Albert Einstein The Feynman Lectures on Physics: The Definitive and Extended Edition by Richard Feynman The Trouble With Physics: The Rise of String Theory, the Fall of a Science, and What Comes Next by L Not Even Wrong: The Failure of String Theory And the Search for Unity in Physical Law by Peter Woit

All times are GMT. The time now is 06:21 AM.