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 110,000 18,000 30,000 Cost per advertisement $1,500 $250 $500 Maximum media usage 11 21 13 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 $23,000, how many commercial messages should be run on each medium to maximize total audience contact? If your answer is zero enter “0”. Advertisement Alternatives No of commercial messages Television Radio Online What is the allocation of the budget among the three media? Advertisement Alternatives Budget ($) 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

Answer 1

Sol:

B) Solution using LINGO is following:

Optimal solution:

T = 11

R = 2

N = 15

Total audience contact = 1,913,000

B) Dual price of promotional budget constraint (Row 2) is 44.

Therefore, additional $ 100 would increase the audience contact by = 44*100 = 4400

New total audience contact = 1913000+4400 = 1,917,400