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 100,000 18,000 40,000 Cost per advertisement $2000 $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 $18,200, how many commercial messages should be run on each medium to maximize total audience contact? What is the allocation of the budget among the three media? Let     T = number of television spot advertisements   R = number of radio advertisements   O = number of online advertisements   Budget ($) T =4 8000 R = 14 4200 O =10 6000   Total Budget = $  18200 What is the maximum total audience that would be reached? Round your answer to the nearest whole number. 105200 By how much would audience contact increase if an extra $100 were allocated to the promotional budget? Round your answer to the nearest whole number. fill in the blank _______________

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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 100,000 18,000 40,000
Cost per advertisement $2000 $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.

 

  1. If the promotional budget is limited to $18,200, 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?

    Let  
      T = number of television spot advertisements
      R = number of radio advertisements
      O = number of online advertisements

      Budget ($)
    T =4 8000
    R = 14 4200
    O =10 6000
      Total Budget = $  18200

    What is the maximum total audience that would be reached? Round your answer to the nearest whole number.

    105200

  2. By how much would audience contact increase if an extra $100 were allocated to the promotional budget? Round your answer to the nearest whole number.

    fill in the blank _______________
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