Problem 4-01 (Algorithmic) The Westchester Chamber of Commerce periodically spon
ID: 431338 • Letter: P
Question
Problem 4-01 (Algorithmic)
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:
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 $27,500, 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.
What is the total audience reached? Round your answer to the nearest whole number.
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.
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Constraint Television Radio Newspaper Audience per advertisement 100000 18000 20000 Cost per advertisement $2000 $300 $600 Maximum media usage 10 25 15Explanation / Answer
Answer :
agree to , 'T' be the run to of TV smidgen advertisements,
'R' be the quantity of broadcasting advertisements, and
'N' be the come to of newspaper advertisements
?Max 100,000T + 18,000R + 40,000N
s.t. 2,000T + 300R + 600N ? 35,600 Budget
T ? 10 (Max Television)
R ? 20 (Max Radio)
N ? 10 (Max News)
-0.5T + 0.5R - 0.5N ? 0 (Max 50% Radio)
0.9T - 0.1R - 0.1N ? 0 (Max 10% Television)
T, R, N, ? 0
By trail and blunder style we get hold of the principles of T,R, and N
If T = 7, R = 17, N = 20, we get
T = 7 * 2000 = $14,000
R = 17 * 300 = $5100
N = 20 * 600 = $12,000
Total = 31,100
Total consultation reached = 100,000 (7) + 18,000 (17) + 40,000 (20) = 1,806,000
b) The dual cost for the financial statement limitation is 50.73 This is achieved by formulating absolute financial statement with the count up spectators 1,806,000/31,100 = 50.73
Thus, a $100 heighten in funds be supposed to present an rise in listeners coverage of approximately 5,037.
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