Problem 9-01 (Algorithmic) The Westchester Chamber of Commerce periodically spon
ID: 3339049 • Letter: P
Question
Problem 9-01 (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:
Constraint
Television
Radio
Newspaper
Audience per advertisement
130000
16500
30000
Cost per advertisement
$2350
$375
$450
Maximum media usage
11
8
15
To ensure a balanced use of advertising media, radio advertisements must not exceed 45% 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 $33350, 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 answer to nearest integer.
Let
T = number of television spot advertisements
R = number of radio advertisements
N = number of newspaper advertisements
Budget $
T =
R =
N =
What is the total audience reached?
By how much would audience contact increase if an extra $100 were allocated to the promotional budget?
Constraint
Television
Radio
Newspaper
Audience per advertisement
130000
16500
30000
Cost per advertisement
$2350
$375
$450
Maximum media usage
11
8
15
Explanation / Answer
Let,
T = number of television spot advertisements
R = number of radio advertisements
N = number of newspaper advertisements
Objective function
Max ZMax =130000T + 16500R + 30000N
s.t. Constraints are
2350T + 375R + 450N 33350 Budget ______________________(1)
T 11 Max TV ______________________(2)
R 8 Max Radio ______________________(3)
N 15 Max News ______________________(4)
-0.55T + 0.45R - 0.55N 0 Max 50% Radio ______________________(5)
0.9T - 0.1R - 0.1N 0 Min 10% TV ______________________(6)
T, R, N, 0
By simplex method, the solution is
T = 11
R = 2
N = 15
Medium
No. of commercial massages
Budget $
Audience
Television spot advertisements T
11
2350x11= 25850
130000x11= 1430000
Radio advertisements R
2
375x2 = 750
16500x2 = 33000
News- paper advertisements N
15
450x15 = 6750
30000x15 = 450000
Total Audience
1913000
If an extra $100 were allocated to the promotional budget, then constraint (1) is
2350T + 375R + 450N 33450
Thus, by simplex method,
T = 11
R = 2.2427
N = 15
Thus, audience is 1917005
Hence, a $100 increase in budget should provide an increase in audience coverage of approximately 4005.
Medium
No. of commercial massages
Budget $
Audience
Television spot advertisements T
11
2350x11= 25850
130000x11= 1430000
Radio advertisements R
2
375x2 = 750
16500x2 = 33000
News- paper advertisements N
15
450x15 = 6750
30000x15 = 450000
Total Audience
1913000
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