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

Constraint	Television	Radio	Newspaper
Audience per advertisement	100000	18000	20000
Cost per advertisement	$2000	$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.

1. If the promotional budget is limited to $31,100, 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 answers to the nearest dollar.

   Let	T = number of television spot advertisements
   	R = number of radio advertisements
   	N = number of newspaper advertisements

   	Budget ($)
   T = ——
   R = ——
   N = ——
   	Total Budget = $

   
   What is the total audience reached? Round your answer to the nearest whole number.
   
   ——————————
2. 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

Max: 100,00T + 18,000R + 20,000S (Maximizing the total audience reached)

Constraints:

1). 2,000T + 300R + 600 S <= 31,100 (budget constraint)

2). 0.5R - 0.5T - 0.5S <= 0 (for the constraint that R has to be <= 50% of total ads)

3). 0.9T - 0.1R - 0.1S >= 0 (for the constraint that T has to be at least 50% of total ads)

4). T <= 10

5). R <= 20

6). S <= 10

7). T, R, S >= 0

Solving this LP, we get

		Budget
T	10.00	20,000
R	19.00	5,700
S	9.00	5,400
Maximum audience reached	1,522,000

If the budget is increased by $100 then making the budget constraint as 31,100 + 100 = 31,200, the maximum audience reached becomes 1,526,222

Increase in audience = 1,526,222 - 1,522,000 = 4,222