5. Formulate only the following goal proble. DEFINE your varlables first! There

Question

5. Formulate only the following goal proble. DEFINE your varlables first! There are decision variables in this problen. An different media-television, radio, and nagazines. The purpose of the advertising progran is to reach as nany of the potential customers as possible. Results of a market study are given below: advertising company wishes to plan an advertising campaign in three Television Radio Nagazines Daytine Prine Tine Cost of an advertising unit 40,000 $85,000 30,000 $15,000 Number of potential custoners reached per unit 400, 000 900,000 500,000 300,000 Number of women customers reached per unit 500,000 400,000 500, 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 1 million exposures should take place among wonen. 2. Advertising on television to be linited to $500,000. 3. Achieve total exposure of 3 million potential custoner 4. Advertising budget should not be exceeded by more than 10. 5. The number of advertising units on radio and nagazine should each be between 8 and 10. 6. At least 3 advertising units to be bought on daytine television, and 2 units during prime tine. P1l

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 to viewers

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

Constraints are as below:-

Advertising budget:- 40,000 x1 + 85,000 x2 + 30,000 x3 + 15000 x4 700,000

40 x1 + 85 x2 + 30 x3 + 15 x4 700

Number of women reached:-

500,000 x1 + 400,000 x2 + 500,000 x3 + 100,000 x4 1,000,000

5 x1 + 4 x2 + 5 x3 + 1 x4 10

Expenses on television:- 40,000 x1 + 85,000 x2 500,000

4 x1 + 8.5 x2 50

Total number of customers:- 400,000 x1 + 900,000 x2 + 500,000 x3 + 300,000 x4 3,000,000

4 x1 + 9 x2 + 5 x3 + 3 x4 30

(Fourth constraint is not clear, please clear it)

Advertising units on radio:- 8x310

Advertising units on magazine:- 8x410

Minimum units for day time:- x13   , x22

Were x1,x2,x3,x4 0

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