1. The Los Angeles Chamber of Commerce periodically sponsors public service seminars and programs. Currently, promotional plans are under way for the year 2006 program and the allocation of the budget to different forms of advertising. The advertising alternatives include television, radio, and newspaper. The goal is to reach the largest possible audience. Audience estimates, costs, and maximum media usage limitations are as shown below:
Constraint Television Radio Newspaper
Audience per advertisement 100,000 18,000 40,000
Cost per advertisement $2,000 $300 $600
Maximum media usage 10 20 10
(# of ads/spots)
To ensure a balanced use of advertising media, radio advertisements must not exceed 50% of the total advertisements authorized. In addition, television should account for at least 10% of the total number of advertisements authorized. If the promotional budget is limited to $18,200, how many commercial messages should be run on each medium to maximize total audience contact? Structure this linear programming problem. (8 points)
All I need to do is structure the problems so I just want to verify my models are correct and any help is appreciated.
I just need to make sure I'm getting this down.
1) Here set my variables x1 x2 and x3 to television, radio, and newspaper respectively.
I set my objective function Z= 100000x1+18000x2+40000x3
subject to constraints:
(1) Budget constraint: 2000x1+300x2+600x3<=18200
(2) Media Usage constraint: Im a bit confused over here. From the chart Im assuming that the max media usage for each alternative can be summed to be the "total advertisements authorized". If this is so then i need to make sure that a. The total ads do not exceed 50 b. radio ads are no more than 25, but then our max is 20 anyway c. at least 5 television ads should be used. Now Im thinking that these are to be seperate constraints:
Is this correct? Where am I going wrong if not? Am I misinterpreting the data?
Thanks a lot