The manager of a restaurant chain in Izmir is trying to decide on the types and amounts of advertising they should use. He has invited officers from the local radio, television stations, and newspaper to describe their audiences. The television station officer says that a TV commercial, which costs 30,000 TL, would reach 50,000 potential customers. The distribution of the audience is as follows: Male Female Elder 10000 10000 Young 10000 20000 The newspaper officer claims to be able to provide an audience of 20,000 potential customers at a cost of 8,000 TL per ad. The distribution of the audience is as follows: Male Female Elder 8000 6000 Young 4000 2000 The radio station officer says that the audience for one of the station’s commercials, which costs 12,000 TL, is 30,000 potential customers. The distribution of the audience is as follows: Male Female Elder 3000 3000 Young 9000 15000 The restaurant chain has the following advertising policy: Use at least twice as many radio advertisement as newspaper advertisement. Reach at least 400,000 potential customers. Reach at least twice as many young people as elder citizens. At least 30% of the audience must be female. Available space limit for the newspaper ads is seven. The restaurant chain wants to know the optimum number of each type of advertising to purchase to minimize total cost. Formulate a linear programming model for this problem. Solve the model by using “Solver”. Interpret the optimum solution and sensitivity report. Suppose additional radio station approaches the restaurant chain and indicates that its commercials, which cost 15000 TL, reach 36000 customers with the following audience distribution: Male Female Senior 4800 7200 Young 8000 16000
The manager of a restaurant chain in Izmir is trying to decide on the types and amounts of advertising they should use. He has invited officers from the local radio, television stations, and newspaper to describe their audiences. The television station officer says that a TV commercial, which costs 30,000 TL, would reach 50,000 potential customers. The distribution of the audience is as follows:
|
Male |
Female |
Elder |
10000 |
10000 |
Young |
10000 |
20000 |
The newspaper officer claims to be able to provide an audience of 20,000 potential customers at a cost of 8,000 TL per ad. The distribution of the audience is as follows:
|
Male |
Female |
Elder |
8000 |
6000 |
Young |
4000 |
2000 |
The radio station officer says that the audience for one of the station’s commercials, which costs 12,000 TL, is 30,000 potential customers. The distribution of the audience is as follows:
|
Male |
Female |
Elder |
3000 |
3000 |
Young |
9000 |
15000 |
The restaurant chain has the following advertising policy:
- Use at least twice as many radio advertisement as newspaper advertisement.
- Reach at least 400,000 potential customers.
- Reach at least twice as many young people as elder citizens.
- At least 30% of the audience must be female.
Available space limit for the newspaper ads is seven. The restaurant chain wants to know the optimum number of each type of advertising to purchase to minimize total cost.
- Formulate a linear programming model for this problem.
- Solve the model by using “Solver”.
- Interpret the optimum solution and sensitivity report.
- Suppose additional radio station approaches the restaurant chain and indicates that its commercials, which cost 15000 TL, reach 36000 customers with the following audience distribution:
|
Male |
Female |
Senior |
4800 |
7200 |
Young |
8000 |
16000 |
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