The manager of a department store in Seattle is attempting to decide on the types and amounts of advertising the store should use. He has invited representatives from the local radio station, television station, and newspaper to make presentations in which they describe their audiences. The television station representative indicates that a TV commercial, which costs $15,000, would reach 25,000 potential customers. The breakdown of the audience is as follows.

            Male   Female
Senior  5,000  5,000
Young  5,000  10,000

The newspaper representative claims to be able to provide an audience of 10,000 potential customers at a cost of $4,000 per ad. The breakdown of the audience is as follows.

             Male   Female
Senior   4,000  3,000
Young   2,000  1,000

The radio station representative says that the audience for one of the station's commercials, which costs $6,000, is 15,000 customers. The breakdown of the audience is as follows.

           Male   Female
Senior  1,500  1,500
Young  4,500  7,500

The store has the following advertising policy.

Use at least twice as many radio commercials as newspaper ads

Reach at least 100,000 customers

Reach at least twice as many young people as senior citizens

Make sure that at least 30% of the audience is female

Available space limits the number of newspaper ads to 7. The store wants to know the optimal number of each type of advertising to purchase to minimize total cost.

a. Formulate a linear programming model for this problem.