Question

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 newspaper. Audience estimates, costs, and maximum media usage limitations are as shown:

Constraint	Television	Radio	Newspaper
Audience per advertisement	100000	18000	40000
Cost per advertisement	$1400	$190	$600
Maximum media usage	10	10	20

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 $20,700, 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
   	N = number of newspaper advertisements

   	Budget ($)
   T =
   R =
   N =
   	Total Budget = $

   
   What is the total audience reached? Round your answer to the nearest whole number.
   
   
   
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.
   

Answer 1

Solution :

Decision variables:

Let

T = No of television spot advertisements

R = No of radio advertisements

N = No of newspaper advertisements

Objective function:

Objective function is to maximize the total audience contact

Z =Max 100000 T + 18000 R + 40000 N

Constraints:

1400 T + 300 R + 600 N <= 22,400 (Budget limit)

T < =10 (Maximum Television usage)

R<= 20 (Maximum Radio usage)

N<= 10 (Maximum Newspaper usage)

R <= 0.5(T+R+N)

Or

-0.5T + 0.5R -0.5N <= 0 (radio advertisements must not exceed 50% of the total number of advertisements)

T>= 0.1(T+R+N)

Or

0.9T – 0.1R-0.1N >= 0

T,R,N >= 0

By using solver we can solve

Budget:

T = 14000

R= 2400

N= 6000

Total audience reached = 13,20,000

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