5. Pormulate only the tollowing goa! problem. DEFIN tirst! There E your variable

Question

5. Pormulate only the tollowing goa! problem. DEFIN tirst! There E your variables aredecision variables in this problem An advertising company wishes to plan an advertising canpaign in thee different media-television, radio, and nagazines. The purpose of the advertising program is to reach as many of the potential customers as possible. Results of a market study are given below: Radio Magazines Television Daytine Prime Time Cost of an advertising unit $40,000 $65,000 $30,000 $15,000 Number of potential customers reached per unit 400,000 900,000 500,000 300,000 Number of wonen customers reached per unit 700,000 400,000 500,000 100,000 The company has an advertising budget of $700,000 and has the following goals to achieve in order of importance: 1. At least 3 million exposures should take place among women. 2. Advertising on television to be limited to $500,000. 3. Achieve total exposure of 4 million potential customer. 4. Advertising budget should not be exceeded by more than 108. 5. The number of advertising units on radio and nagazine should each be between 5 and 10. 6. At least 3 advertising units to be bought on daytime television, and 2 units during prime time

Explanation / Answer

There are 4 decision variables in the problem

x1 = No. of units to be advertised through television ( Day time)

x2 = No. of units to be advertised through television ( Prime time)

x3 = No. of units to be advertised on Radio

x4 = No. of units to be advertised on magazine

Definition of problem

1. 700000x1+ 400000X2+500000x3+100000x4 => 3000000

2. 40000 x1+65000x2 <= 500000

3. 400000x1+ 900000X2+500000x3+300000x4 = 4000000

4. 40000x1+ 65000X2+30000x3+15000x4 <= 770000

5. 5<=x3+x4 <=10

6. x1=>3 and x2=>2

Objective function is to Minimize cost

i.e. Min. 40000x1+ 65000X2+30000x3+15000x4

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