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

Constraint	Television	Radio	Online
Audience per advertisement	200,000	36,000	80,000
Cost per advertisement	$2,000	$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.

(a) If the promotional budget is limited to $22,800, how many commercial messages should be run on each medium to maximize total audience contact?

Television:

Radio:

Online:

What is the allocation of the budget among the three media, and what is the total audience reached?

Television Budget (in dollars):

Radio Budget (in dollars):

Online Budget (in dollars):

Total Audience:

(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.)

Answer 1

(a) If the promotional budget is limited to $22,800, how many commercial messages should be run on each medium to maximize total audience contact?
Television:		4		at least 10%
Radio:		19		Not more than 50 %
Online:		15		Balance
What is the allocation of the budget among the three media, and what is the total audience reached?			2,684,000
Television Budget (in dollars):		$8,000
Radio Budget (in dollars):		$5,700
Online Budget (in dollars):		$9,000
Total Audience:		2,684,000
(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.)
Out of $22,800, Amount allocated is $22,700 because minimum advertisement cost on Radio is $300. Even after increasing $ 100 in advertisement budget
The balance in hand will be $ 200 ($100 Balance+$100 new allocation), Minimum amount required is $300. so no additional audience will be reached.
Constraint		Television	Radio	Online
Audience per advertisement		200,000	36,000	80,000
Cost per advertisement		$2,000	$300	$600
Maximum media usage		10	20	10
Let Maximum Advertisement (No of advertisement)	100	10	50	40	Allocated as per requirement of question
Maximum advertisement cost for allocation of advertisement no		20,000	15,000	24,000	No. of advertisement * Cost per advertisement
Allocated advertisement budget in the ratio of preceeding line		7,729	5,797	9,275	$ 22,800*20000/Total advertisement cost of all the media, calculated above
No of Advertisement		3.86	19.32	15.46	Allocated advertisement budget/cost per advertisement
No of Advertisement converted to whole no.		4	19	15	Total advertisement 38 nos.
Cost of advertisement		$8,000	$5,700	$9,000	No. of advertisement*Cost per advertisement
Total audience		800,000	684,000	1,200,000	No. of advertisement*Audience per advertisement