Chapter 3.2, Problem 12E

Political Campaign—-Resource Allocation A local politician has budgeted at most $80,000 for her media campaign. She plans to distribute these funds between TV ads and radio ads. Each one-minute TV ad is expected to be seen by 20,000 viewers, and each one-minute radio ad is expected to be heard by 4000 listeners. Each minute of TV time costs $8000, and each minute of radio time costs $2000. She has been advised to use

at most 90% of her media campaign budget on television ads.

(a) Fill in the following chart.

	One-Minute TV Ads	One-Minute Radio Ads	Available
Cost
Audience reached

(b) Let x be the number of minutes of TV ads, and let y be the number of minutes of radio ads. Refer to the chart, and give an inequality that x and y must satisfy due to the amount of money available.

(c) Give the inequality that x must satisfy due to the limitation on the amount of money to be spent on TV ads. Also, give the inequalities that x and y must satisfy because x and y cannot be negative.

(d) Give an expression for the total audience reached by x minutes of TV ads and y minutes of radio ads.

(e) Graph the feasible set for the political campaign problem.