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Posted By: sunil Member Level: Diamond Posted Date: 01 Jul 2008
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2007 Jawaharlal Nehru Technological University Chemical engineering IV B.Tech II Semester Supplementary Examinations, June 2007 OPERATIONS RESEARCH Question paper
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Code No: RR420804
Set No. 1
IV B.Tech II Semester Supplementary Examinations, June 2007
OPERATIONS RESEARCH
(Chemical Engineering)
Time: 3 hours
Answer any FIVE Questions
All Questions carry equal marks
? ? ? ? ?
Max Marks: 80
1. Write an essay on Scope, Methodology and Phases of Operations Research.
2. (a) Explain the use of arti?cial variable and its use in linear programming.
[16]
(b) An animal feed company must produce 200 Kg of a mixture containing of
ingredients A and B respectively. Ingredient A Costs Rs. 3/- per Kg. And B
costs Rs. 8/- per Kg. No more than 80 Kg of A can be used and at least 60
Kg of B must be used. Find how much of each ingredients should be used if
the company wants to minimize cost.
[16]
3. Company has to produce ?ve jobs, each of which must go through the two machines
in the order AB. Processing times are given in the table below:
Job no:
1 2 3 4 5
Machine A 10 2 18 6 20
Machine B 4 12 14 16 8
Determine a sequence for the ?ve jobs that will minimize the total elapsed time.
[16]
4. (a) Explain how the theory of replacement is used in replacement of items that
fails suddenly.
(b) The purchase price of a machine is Rs.3,000/- and its running cost is given in
the table below. If the discount rate is Rs0.90/- ,?nd at what age the machine
should be replaced?
[4+12]
Year :
1
2
3
4
5
6
7
Running Cost in Rs. 500 600 800 1000 1300 1600 2000
5. (a) List the characteristics of competitive games.
[4]
(b) Two companies A and B are competing for the same product. Their di?erent
strategies are given in the following pay o? matrix.
Company A
A1 A2 A3
Company B B1 2 -2 3
B2 -3 5 -1
[12]
What are the best strategies for both the companies? Find out the value of
the Game.
6. What do you mean by Poisson process. Derive the Poisson distribution given that
the probability of single arrival during a small time intraval ? t is ??t and that of
more than one arrival is negligible where ? is mean arrival rate.
[16]
7. (a) A Company uses annually 48000 units : of a raw material costing Rs. 1.20
/ unit placing each order costs Rs. 45 /- carrying cost is 1.5 % /year of the
average inventory. Find E.O.Q and Minimum cost.
(b) Discuss the impact on lot size if shortages are allowed.
[12]
[4]
8. An industrialist is interested in allocating six salesmen among its three marketing
zones so that the total pro?t can be maximized . The expected yearly pro?t (in
thousands of rupees) from the allocation of salesmen in each zone are tabulated
below:
Number of salesmen Zone A Zone B Zone C
[16]
0
1
2
3
4
5
6
0
15
35
60
90
110
125
0
20
40
70
110
140
150
0
35
60
85
110
130
150
Answer the following questions using dynamic programming:
(a) What is the nest allocation of salesmen among the zones
(b) What is the second best solution?
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