Carmen, the manager of a department store in Puerto Rico, is attempting to decid
ID: 404445 • Letter: C
Question
Carmen, the manager of a department store in Puerto Rico, is attempting to decide on the types and amounts of advertising the store should use. She has invited representatives from a local radio station, a television station, and a newspaper to make presentations in which they describe their audiences. The television station representative indicates that a TV commercial, which costs $20,000 per spot, would reach 35,000 potential customers. 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 radio station representative says that the audience for one of the station
Carmen, the manager of a department store in Puerto Rico, is attempting to decide on the types and amounts of advertising the store should use. She has invited representatives from a local radio station, a television station, and a newspaper to make presentations in which they describe their audiences. The television station representative indicates that a TV commercial, which costs $20,000 per spot, would reach 35,000 potential customers. 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 radio station representative says that the audience for one of the station's commercials, which costs $5,000 per spot, is 15,000 customers. The breakdown of the audience (in thousands) is as follows. The store has the following advertising policy: ? Use at least twice as many radio commercials spots as newspaper ads and TV commercial spots, combined. ? Reach at least 120,000 customers. ? Reach at least twice as many young people as senior citizens. ? Make sure that at least 25% of the total audience is female. Available space limits the number of newspaper ads to seven. Carmen wants to know the optimal number of each type of advertising to purchase.Explanation / Answer
Hi. The question has a bit of a flaw. It says 35,000 customers for television. But the break-up shows only 25,000.
Assuming that the TV commercial reaches 25,000 customers, the formulation of the prolem is as follows:
Let there be number of television ads = x, newspaper ads = y, radio ads = z.
Hence the objective is: Minimize the cost: 20,000 x + 4,000 y + 5,000 z
Conditions:
z >= 2x;
z >= 2y;
25000 x+ 10000y + 15000z >= 120000;
(15000x + 4000y + 9000z) >= (25/100)*25000 x+ 10000y + 15000z ;
y <= 7.