5. Forulate only the following goal problem. DEFINE your variables first- There

Question

5. Forulate only the following goal problem. DEFINE your variables first- There are decision variables in this problem. An advertising company wishes to plan an advertising campaign in three different nedia-television, radio, and nagazines. The purpose of the advertising program is to reach as nany of the potential custoners as possible. Results of a market study are given below: Television Radio Magazines Daytine Prine Time Cost of an advertising unit $50,000 575,000 $30,000 915,000 Number of potential customers reached per unit 400,000 900,000 500,000 300,000 Number of wonen customers reached per unit 300,000 500,000 200,000 100,000 The conpany has an advertising budget of $600,000 and has the following goals to achieve in order of importance: 1. At least 2 million exposures should take place among women 2. Advertising on television to be limited to $500,000 3. Achieve total exposure of 5 million potential customer. 4. Advertising budget should not be exceeded by more than 108. 5. The number of advertising units on radio and magazine should each be between 5 and 15. 6. At least 3 advertising units to be bought on daytime television, and units during prime time

Explanation / Answer

Let us consider that x1, x2,x3, and x4 represents the advertising units which are to be bought on television daytime, prime time , radio and magazine

The main objective of this problem is to maximize the total number of viewers

Maximize Z =10(4x1 + 9x2 + 5x3 + 3x4)

Constraints are as below:-

Advertising budget:- 50,000 x1 + 75,000 x2 + 30,000 x3 + 15000 x4 600,000

5 x1 + 7.5 x2 + 3 x3 + 1.5 x4 60

Number of women reached:-

300,000 x1 + 500,000 x2 + 200,000 x3 + 100,000 x4 2,000,000

3 x1 + 5 x2 + 2 x3 + 1 x4 20

Expenses on television:- 50,000 x1 + 75,000 x2 500,000

5 x1 + 7.5 x2 50

Total number of customers:- 400,000 x1 + 900,000 x2 + 500,000 x3 + 300,000 x4 5,000,000

4 x1 + 9 x2 + 5 x3 + 3 x4 50

Budget exceeding:- 50,000 x1 + 75,000 x2 + 30,000 x3 + 15000 x4 660,000

5 x1 + 7.5 x2 + 3 x3 + 1.5 x4 66

Advertising units on radio:- 5x315

Advertising units on magazine:- 5x415

Minimum units for day time:- x13   , x22

Where x1,x2,x3,x4 0

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