Ottawa City Council is trying to decide how to allocate its promotional budget of $18,200 for this year’s To-Die-For Donut Festival. Advertising alternatives include television, radio, and newspaper. For television, the estimated audience per advertisement is 100,000 people and the average cost per advertisement is $2,000. For radio, the estimated audience per advertisement is 18,000 people and the average cost per advertisement is $300. While, for newspaper, the estimated audience per advertisement is 40,000 people and the average cost per advertisement is $600. To satisfy local sensibilities in the broader public relations industry, the city feels that that there should be limits on how many advertisements should be produced by each type of media. Specifically, it is felt that there should be no more than 10 television advertisements, no more than 20 radio advertisements, and no more than 10 newspaper advertisements. Finally, to satisfy the Ontario Advertising Standards Council requirements that advertising by public entities should be balanced, no more than 50% of the total number of advertisements should be on radio and at least 10% of the total number of advertisements should appear on television.

Formulate an LP that can be used to determine how the promotional budget should be allocated among the three types of advertising alternatives in order to maximize the total audience contact.