2. (18 pts) (Media selection) The Samulson Co. has a promotional plan for its new product. Advertising alternatives include television, radio, magazine and newspaper. Audience estimates, costs, and maximum media usage are as shown.

Constraint	Television	Radio	Magazine	Newspaper
Audience reached per ad	1,600	1,300	1,000	2,200
Cost ($) per ad	1,400	400	700	1,200
Maximum media available	40	45	55	70

Samulson has the promotional budget of $175,000. To ensure a balanced use of advertising media, radio advertisements must not exceed 35% of the total number of advertisements. Television should account for at least 30% of the total number of advertisements. Television and radio together may not exceed twice of the total of magazine and newspaper advertisements. In addition, the company has decided to use at least 20 ads in each media.

Set up a linear programming model to maximize audience reached.