lyom Formulate only the tollowing goal problem. DEFINE your variables 5. firat!
ID: 376791 • Letter: L
Question
lyom Formulate only the tollowing goal problem. DEFINE your variables 5. firat! There are decision variabloas in this problem. An advertising conpany wishes to plan an advertising campaign in three different media-television, radio, and magazines. 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: Television Radio Magazines Daytime Prime Time Cost of an advertising unit $60,000 $75,000 $30,000 $15,000 Number of potential customers reached per unit 400,000 900,000 300,000 200,000 Number of women customers reached per unit 300,000 400,000 200,000 400,000 The company has an advertising budget of $800,000 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 $400,000. 3. Achieve total exposure of 3 million potential customer. 4. Advertising budget should not be exceeded by more than 20%. 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 dayt ime television, and 2 units during prime time.Explanation / Answer
There are 4 decision variables in the problems.
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 + 3x3 + 2x4)
Constraints are as below:-
Advertising budget:- 60,000 x1 + 75,000 x2 + 30,000 x3 + 15000 x4 800,000
6 x1 + 7.5 x2 + 3 x3 + 1.5 x4 80
Number of women reached:-
300,000 x1 + 400,000 x2 + 200,000 x3 + 400,000 x4 2,000,000
3 x1 + 4 x2 + 2 x3 + 4 x4 20
Expenses on television:- 60,000 x1 + 75,000 x2 400,000
6 x1 + 7.5 x2 40
Total number of customers:- 400,000 x1 + 900,000 x2 + 300,000 x3 + 200,000 x4 3,000,000
4 x1 + 9 x2 + 3 x3 + 2 x4 30
Budget exceeding:- 60,000 x1 + 75,000 x2 + 30,000 x3 + 15000 x4 960,000
6 x1 + 7.5 x2 + 3 x3 + 1.5 x4 96
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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