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	400,000	72,000	160,000
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 $20,500, 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

1. Given that audience per advertisement for telivision is: $400,000, radio: $72,000 and online is: $160,000,

represented by the allocation of spot as T, R and O, the objective function is equal to:

maximum of: $400,000*T + $72,000*R + $160,000*O.

2. Also, the cost per advertisement given the promotional budget is limited to: $20,500 forms the following objective function:

2000*T + 300*R + 600*O <= $20,500

3. The maximum media usage:

T< 10, R<20 and O< 10.

4. Given that the maximum radio advertisements would be 50% and same is 10% for TV, therefore:

TOTAL AUDIENCE REACH: 2000*4.200 +  300*5.3 + 600*8 = 14760.

R<= 0.5*(T+O)

and T>= 0.1(T + R + O)

we will make use of the command: 'solver' in excel,

therefore:

t= 4.2

R= 5.2

O=8

Therefore total cost = 14760

b) no change in the audience contact if $100 more is allocated.