s. Formulate only the following goal problem. DBE first! There are different med

Question

s. Formulate only the following goal problem. DBE first! There are different media-television, radio, and nagazines. The puztyisto advertising program is to reach as many of the potentia possible. Results of a narket study are given below An advertising company vishes to plan an advertising os decision variables in this problemn. DEFINE your variables campaign in three purpose of the potential customers as Television Radio Magazines Daytime Prime Time cost of an advertising unit $40,000 $85,000 $30,000 $15,000 Number of potential customers reached per unit 400,000 900,000 500,000 300,000 Number of women customers 500,000 400,000 500,000 100,000 reached per unit 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 women. 2. Advertising on television to be limited to $500, 000. 3. Achieve total exposure of 3 million potential customer. 4. Advertising budget should not be exceeded by more than 10% 5. The ising units on radio and magazine should each be number of advert between 8 and 10. 6. At least 3 advertising units to be bought on daytine television, and 2 units during prime time.

Explanation / Answer

in the question it is being asked formulation of the above markeinng problem into linear programming.

FOllowing is te formulation as per the given conditions

Mximize (total potential customer reached) Z= 400000x1+900000x2+500000x3+300000x4

Subject to the constraints

(a)                 advertising budget constrain

40000x1 + 85000x2+30000x3+15000x4 =<700000

               

(b)                 number of women customer reached by the advertising compaign constraint

500000x1+400000x2+500000x3+100000x4>=1000000

(c)                 TV advertising constraint

40000x1 + 85000x2 =<500000

x1>=3

x2>=2

(d)                 radio and magazine advertising constraint

8=<x3=<10

8=<x4=<10

and                         x1,x2,x3,x4>=0

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