The Westchester Chamber of Commerce periodically sponsors public service seminars and programs. Currently, promotional plans are under way for this year’s program. Advertising alternatives include television, radio, and online. Audience estimates, costs, and maximum media usage limitations are as shown: Constraint Television Radio Online Audience per advertisement 100000 18000 40000 Cost per advertisement $1400 $300 $600 Maximum media usage 10 20 10 To ensure a balanced use of advertising media, radio advertisements must not exceed 50% of the total number of advertisements authorized. In addition, television should account for at least 10% of the total number of advertisements authorized. If the promotional budget is limited to $21,200, how many commercial messages should be run on each medium to maximize total audience contact? What is the allocation of the budget among the three media? If required, round your answers to the nearest dollar. Let T = number of television spot advertisements R = number of radio advertisements O = number of online advertisements

The solution is given as such that ads run on Television, Radio and Online are 10, 4 and 10 respectively for the maximum audience of 1472000 such that the  budget allocation is 14000, 1200 and 6000 between Television, Radio and Online respectively.

Explanation:

For the constraint analysis the data is given as below

Constraint               Television             Radio                Online

Audience                   100000              18000               40000

  Cost                          $1400                $300                $600

 Max Media                     10                      20                     10

Let's suppose

So the function to maximize is given as

Z=100000T+18000R+40000O

The constraints are

1400T+300R+600O ≤21200

T≤10

R≤20

O≤10

Radio advertisements must not exceed 50% of the total number of advertisements authorized.

R≤0.5(T+R+O)

In addition, television should account for at least 10% of the total number of advertisements authorized.

T≥0.1(T+R+O)

Using the following spreadsheet the solution is obtained using following steps

The solution is given as such that

T=10

R=4

O=10

The total maximized audience is 1472000

The budget allocation is 14000, 1200 and 6000 between Television, Radio and Online respectively.

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