The advertising alternatives for a company include television, radio, and newspaper advertisements. The costs and estimates for audience are shown in table 2. The local newspaper limits the number of weekly advertisements from a single company to ten. Moreover, in order to balance the advertising among the three types of media, no more than half of the total number of advertisements should occur on the radio, and at least 10% should occur on television. The weekly advertising budget is $18,200.
Table 2
Television Newspaper Radio
Cost per advertisement $ 2,000 $ 600 $ 300
Audience per advertisement 100,000 40,000 18,000
Find the mathematical model for the optimization problem for how many advertisements should be run in each of the three types of media to maximize the total audience.