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	120000	20000	37000
Cost per advertisement	$1500	$210	$430
Maximum media usage	12	25	10

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 $26080, 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?

Answer 1

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 120000 T + 20000 R + 37000 N

Constraints:

1500 T + 210 R + 430 N <= 26080 (Budget limit)

T < =12 (Maximum Television usage)

R<= 25 (Maximum Radio usage)

N<= 10 (Maximum Newspaper usage)

R <= 0.45(T+R+N)

Or

-0.45T + 0.55R -0.45N <= 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 = 18000

R= 3780

N= 4300

Total audience reached=21,70,000

No audience contact increase if an extra $100 were allocated to the promotional budget