Download JNTUH (Jawaharlal nehru technological university) MCA (Master of Computer Applications) 3rd Sem (Third Semester) Regulation-R19 2021 July-August 863AB Operations Research Previous Question Paper
R19
Code No: 863AB
2021
JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD
MCA III Semester Examinations, July/August - 2021
OPERATIONS RESEARCH
Time: 3Hours
Max.Marks:75
Answer any five questions
All questions carry equal marks
- - -
1.
Solve the following LPP using the simplex method.
Max Z=x1-x2+3x3
Subject to x1+x2+x310
2x1-x33
2x1-2x2+3x30
and x1, x2, x30
[15]
2.
The standard weight of a special purpose brick is 5 kg and it contains two basic
ingredients X and Y. X costs Rs. 5 per kg and Y costs Rs. 8 per kg. Strength
considerations dictate that the brick contains not more than 4 kg of X and a minimum
of 2 kg of Y. Since the demand of the product is likely to be related to the price of the
brick, find graphically the minimum cost of the brick satisfying the above conditions.
[15]
3.
The maintenance cost and resale value per year of a machine whose purchase price is
Rs. 7000 is given below, when should the machine be replaced?
[15]
Year
1
2
3
4
5
6
7
8
Maintenance cost in 900
1200 1600 2100 2800 3700 4700
5900
Rs.
Resale value in Rs.
4000 2000 1200 600
500
400
400
400
4.
A machine operator has to perform two operations turning and threading on a number
of different jobs. The time required to perform these operations for each job is known.
Determine the order in which the jobs should be processed in order to minimize the
total time required to complete all the jobs.
[15]
Machine/Job 1
2
3
4
5
6
A
3
12
5
2
9
11
B
8
10
9
6
3
1
5.
Solve the following travelling salesman problem and find the shortest possible path.
[15]
2021 A B C D E
A
3
6
2
3
B
3
5
2
3
C
6
5
6
4
D
2
2
6
6
E
3
2
4
6
6.
Solve the game whose payoff matrix for the player A is given in table.
[15]
Player B
I
II
III
Player
I
-2
15
-2
A
II
-5
-6
-4
III
-5
20
-8
7.
In a railway yard goods train arrive at a rate of 30 trains/day. Assuming that the inter-
arrival time follows an exponential distribution and the service time distribution is also
exponential with an average 36 minutes. Calculate the following:
a) The average number of trains in the queue.
b) The average number of trains in the system.
c) The probability that number of trains in the system exceeds 10.
[15]
8.a)
State the Bellman's Principle of Optimality.
b)
What are the applications of dynamic programming?
[7+8]
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This post was last modified on 17 March 2023