Formulate the Linear programming model for the problem to maximize the total expected effective exposure

a) Magnate Ventures an advertising agency is preparing an advertising campaign for a group of agencies. These agencies have decided that their target customers should have the following characteristics with importance (weightage) as given below.

characteristics Weightage(%)
Age
Annual income

female

25 – 45 years
Above Sh. 80,000

Married

20
40

40

The agency has made a careful analysis of three media and has compiled the following data:

Data Item Media
Magazine Radio Television
Audience size (‘000)
Cost per advertisement (Sh.)

Min. no. of advertisements allowed

800
10,000

15

1000
30,000

10

1500
100,000

10

Max. no. of advertisements allowed
Reader Characteristics

Age 25 – 45 years

Annual income above Sh. 80,000

Females married

25
70%

60%

45%

15
60%

50%

40%

15
50%

40%

30

The advertising agency has earmarked a budget of Sh. 1000,000 for this purpose.

Formulate the Linear programming model for the problem to maximize the total expected

effective exposure. (12marks)

b) Find the local maximum and local minimum values, if any, of the function:

y = (8marks


 

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