Marketing problem
10. The manager of a department store in Adama 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.

a. The television station representative indicates that a TV commercial, which costs Birr 15,000, would reach 25,000 potential customers. The break down of the audience is as follows.

Male Female

Old 5,000 5,000
Young 5,000 10,000

b. The news paper representative claims to be able to provide an audience of 10,000 potential customers at a cost of Birr 4000 per ad. The break down of the audience is as follows.

Male Female

Old 4,000 3,000
Young 2,000 1,000



c. The radio station representative says that the audience for one of the station’s commercials, which costs Birr 6000, is 15,000 customers. The break down of the audience is as follows.


Male Female

Old 1,500 1,500
Young 4,500 7,500


The store has the following advertising policy:
a. Use at least twice as many radio commercials as news paper ads.
b. Reach at least 100,000 customers
c. Reach at least twice as many young people as old people
d. Make sure that at least 30% of the audience is women.

Available space limits the number newspaper ads to 7. The store wants to know the optimal number of each type of advertising to purchase to minimize total cost.
Required:
Formulate appropriate linear programming model.