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 100,000 16,000 35,000 Audience per advertisementCost per advertisement $1,500 $250 $650Maximum media usage 10 24 14To 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.(a) If the promotional budget is limited to $18,400, how many commercial messages should be run on each medium to maximize total audience contact? If your answer is zero enter “0”.Advertisement Alternatives No of commercial messagesTelevision _______________ Radio _______________Online _______________What is the allocation of the budget among the three media?Advertisement Alternatives Budget ($)__________________Television $________________Radio $________________ Online $________________What is the total audience reached?________________(b) 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.Increase in audience coverage of approximately _______________ 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:ConstraintTelevisionRadioOnlineAudience per advertisement100,00016,000 35,000Cost per advertisement$1,500$250$650Maximum media usage102414To 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 advertisementsauthorized.(a) If the promotional budget is limited to $18,400, how many commercial messages should be run on each medium to maximize total audience contact? If your answer is zero enter "0".No of commercialAdvertisement AlternativesmessagesTelevisionRadioOnlineWhat is the allocation of the budget among the three media?Advertisement AlternativesBudget ($)TelevisionRadio$Online$What is the total audience reached?(b) 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.Increase in audience coverage of approximately

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 100,000 16,000 35,000 Audience per advertisement Cost per advertisement $1,500 $250 $650 Maximum media usage 10 24 14 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. (a) If the promotional budget is limited to $18,400, how many commercial messages should be run on each medium to maximize total audience contact? If your answer is zero enter “0”. Advertisement Alternatives No of commercial messages Television _______ Radio _ Online _ What is the allocation of the budget among the three media? Advertisement Alternatives Budget ($) Television $ Radio $ Online $ What is the total audience reached? (b) 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. Increase in audience coverage of approximately _____

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter2: Introduction To Spreadsheet Modeling

Section: Chapter Questions

Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...

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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
100,000 16,000 35,000
Audience per advertisement

Cost per advertisement
$1,500 $250 $650

Maximum media usage
10 24 14

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.

(a) If the promotional budget is limited to $18,400, how many commercial messages should be run on each medium to maximize total audience contact? If your answer is zero enter “0”.

Advertisement Alternatives No of commercial messages

Television _______________
Radio _______________
Online _______________

What is the allocation of the budget among the three media?
Advertisement Alternatives Budget ($)__________________

Television $________________
Radio $________________
Online $________________

What is the total audience reached?________________

(b) 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.
Increase in audience coverage of approximately _______________

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
16,000 35,000
Cost per advertisement
$1,500
$250
$650
Maximum media usage
10
24
14
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.
(a) If the promotional budget is limited to $18,400, how many commercial messages should be run on each medium to maximize total audience contact? If your answer is zero enter "0".
No of commercial
Advertisement Alternatives
messages
Television
Radio
Online
What is the allocation of the budget among the three media?
Advertisement Alternatives
Budget ($)
Television
Radio
$
Online
$
What is the total audience reached?
(b) 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.
Increase in audience coverage of approximately

Expert Solution

Step 1: LP model

T = Number of Television messages

R = Number of Radio messages

O = Number of Online messages

Objective function:

Max Z = $100, 000 T + 16, 000 R + 35, 000 O$

Constraints:

Budget: $1, 500 T + 250 R + 650 O \leq 18, 400$

Maximum Media usage: $T \leq 10 R \leq 24 O \leq 14$

Radio must not be more than 50% of the total: $R \leq 0.5 (T + R + O) R \leq 0.5 T + 0.5 R + 0.5 O - 0.5 T + 0.5 R - 0.5 O \leq 0$

Television must be at least 10% of the total: $T \geq 0.1 (T + R + O) T \geq 0.1 T + 0.1 R + 0.1 O 0.9 T - 0.1 R - 0.1 O \geq 0$

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