Page 29 - DCOM303_DMGT504_OPERATION_RESEARCH

Operations Research

Notes Solution:
Let x represent the advertising on prime day on television
1
x represent the advertising on prime time on television
2
x represent the campaign on radio
3
x represent the campaign on magazine.
4
Therefore 4,00,000x represent the potential customers on advertising on prime day on television.
1
9,00,000x represent the potential customers on prime time on television.
2
5,00,000x be the potential customers on advertising on Radio.
3
2,00,000x be the potential customers on advertising in Magazines.
4
Hence the objective function is given by

Maximum ‘Z’ = 4,00,000x + 9,00,000x + 5,00,000x + 2,00,000x (Subject to constraints)
1 2 3 4
40,000x + 75,000x + 30,000x + 15,000x  8,00,000 (Advertising constraint)
1 2 3 4
40,000x + 75,000x  5,00,000 (Advertising on television constraint)
1 2
3,00,000x + 4,00,000x + 2,00,000x + 1,00,000x  2 Million (No. of women
1 2 3 4
customers constraint)
x  3
1
x  2 No. of unit constraints)
2
5  x3  10
5  x  10 (Minimum no. of advertisements allowed constraints)
4
Therefore x , x , x , x  0 (Non-negativity constraints)
1 2 3 4

Example: A city hospital has the following daily requirements of nurses at the minimal
level:

Clock Time Minimal no. of nurses
Period
(24 hours a day) required
1 6 a.m. – 10 a.m. 2
2 10 a.m. – 2 p.m. 7
3 2 p.m. – 6 p.m. 15
4 6 p.m. – 10 p.m. 8
5 10 p.m. – 2 a.m. 20
6 2 a.m. – 6 a.m. 6
Nurses report to the hospital at the beginning of each period and work for 8 consecutive hours.

The wants to determine minimal number of nurses to be employed, so that there will be sufficient
number of nurses available for each period.
Formulate this as LP model by setting up appropriate constraints and objective function.

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