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 18,000 40,000
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 percent of the total number of advertisements authorized. In addition, television should account for at least 10 percent of the total number of advertisements authorized.

a. If the promotional budget is limited to $18,200, 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, and what is the total audience reached?
b. By how much would audience contact increase if an extra $100 were allocated to the promotional budget?

As cost per audience contact is lowest from television advertising, therefore 10 advertisement will be given in Television media, therefore budget allocated to television = 1400*10 = $14,000

Thereafter advertisement will be given in news paper, therefore budget allocated to newspaper for 10 advertisement = 600*10 = $6,000

Remaining budget will be allocated to radio = $22,400 - $14,000 - $6,000 = $2,400

Nos of advertisement in radio = $2,400 / $300 = 8

Budget allocated to television = $14,000

Budget allocated to radio = $2,400

Budget allocated to news paper = $6,000

Solution b:

Total audience reached = (100000*10) + (18000*8) + (40000*10) = 1544000

Solution c:

If $100 extra were allocated to the promotional budget. then same will be used for radio advertisement

Increase in audience contact = Extra cost / Cost per audience contact = $100 / $0.0167 = 5988 audience contact