The manager of a department store in Seattle is attempting to decide on the types and amounts pf advertising the store should use He has invited representatives from the local radio station, TV station, and newspaper station to make presentations in which they describe their audiences The TV station representatives indicated 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 1,000 The newspaper representatives claims to be able to provide the audience pf 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 representatives says that the audience for one of the stations commercials, which costs $6000, is 15000 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 seven 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 b solve the model by using computer c suppose a second radio station approaches the department store and indicates that its commercials, which cost $7,500 reach 18,000 customers with the following demographic breakdown Male Female Senior 2,400 3,600 Young 4,000 8,000 If the store considered this station along with the other media alternatives, how would this affect the solution Formulate linear program xi number of ads of type i the store uses i(1 Tv, 2 Newspaper, 3 Radio) Min 15000x1 10000x2 x3 x4 s t x3 x4 2 1 ( can you tell how this would go into QM) 25000x1 100000x2 x3 x4 Finish problem please and explain

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The manager of a department store in Seattle is attempting to decide on the types and amounts pf advertising the store should use. He has

The manager of a department store in Seattle is attempting to decide on the types and amounts pf advertising the store should use. He has invited representatives from the local radio station, TV station, and newspaper station to make presentations in which they describe their audiences. The TV station representatives indicated 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 1,000

The newspaper representatives claims to be able to provide the audience pf 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 representatives says that the audience for one of the stations commercials, which costs $6000, is 15000 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 seven. 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.

b. solve the model by using computer

c. suppose a second radio station approaches the department store and indicates that its commercials, which cost $7,500 reach 18,000 customers with the following demographic breakdown:

Male Female

Senior 2,400 3,600

Young 4,000 8,000

If the store considered this station along with the other media alternatives, how would this affect the solution?

Formulate linear program:

xi- number of ads of type i the store uses; i(1-Tv, 2-Newspaper, 3-Radio)

Min 15000x1 + 10000x2 -x3 -x4

s.t.

x3/x4>= 2/1 ( can you tell how this would go into QM)

25000x1 +100000x2 -x3-x4

Finish problem please and explain