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Media Buying
A company wants its advertisements to reach at least 1.5 million people through different media.
There is a maximum number of ad impressions considered effective in each medium. How should
the company advertise to minimize total cost while satisfying the limits on reach and frequency?
Media Requirements      
  TV Radio Mail Newspaper
Audience Size 50,000 25,000 20,000 15,000
Cost / Impression $500 $200 $250 $125
Max Impressions 20 15 10 15
Investments          
  TV Radio Mail Newspaper Total
Amount $0 $0 $0 $0 $0
Impressions 0 0 0 0  
Audience 0 0 0 0 0
Problem          
A company wants its advertisements to reach at least 1.5 million people. It is considering advertising
through TV, radio, direct mail, and newspapers. Each medium has a certain cost per run of an ad,
a certain audience that will see the ad, and a maximum number of ad impressions before response
to the ad falls off too much. How should the company advertise in order to reach its target audience
at the lowest possible cost?        
           
Solution          
1) The variables are the amounts of money to spend on each medium. In worksheet Media these
are given the name Investments.        
2) The constraints are very simple.        
  Investments >= 0 via the Assume Non-Negative option  
  Impressions <= Max_Impressions for each medium  
  Total_Audience >= 1500000    
3) The objective is to minimize total cost. In worksheet Media this is defined as Total_investment.
           
Remarks          
Often, there are discounts for placing ads with greater frequency in different media. This could be
expressed in a model with a 'piecewise-linear' constraint, using binary integer variables.

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