Download JNTUH (Jawaharlal nehru technological university) MCA (Master of Computer Applications) 2nd Sem (Second Semester) Regulation-R15 2019 December 821AJ Operations Research Previous Question Paper
R15
Code No: 821AJ
JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD
MCA II Semester Examinations, December - 2019
OPERATIONS RESEARCH
Time: 3hrs
Max.Marks:75
Note: This question paper contains two parts A and B.
S Part A is compulsory which carries 25 marks. Answer all questions in Part A.
Part B consists of 5 Units. Answer any one full question from each unit. Each
question carries 10 marks and may have a, b, c as sub questions.
PART - A
5 ? 5 Marks = 25
1.a)
State the various types of OR models according to structure.
[5]
b) State the variants of assignment problem. How are they resolved?
[5]
c) State and explain Johnson's algorithm for n jobs and two machine problems.
[5]
d) State and explain Bellman's principle of optimality.
[5]
e) State the functions of inventory.
[5]
PART - B
5 ? 10 Marks = 50
2.a)
Define OR. State and explain various phases of OR.
b)
Solve the following LPP by using the graphical method.
[4+6]
Minimize Z 6x 4x
1
2
st 2x 3x 30
1
2
3x 2x 24
1
2
x x 3
x 0 i
1
2
i
OR
3.
Solve the following LPP problem by two-phase method
Max Z 4x 3x 5x
1
2
3
st x 3x 2x 10
1
2
3
2x 2x x 6
1
2
3
x 2x 3x 14, x 0 i
1
2
3
i
[10]
4.
A company has three factories I, II, III and four warehouses 1, 2, 3, 4. The transportation
cost (in Rs.) per unit from each factory to each ware house is given in table. The
requirements of each warehouse and the capacity of each factory are given below.
1
2
3
4
Availability
I
25
17
25
14
400
II
15
10
18
24
600
III
16
20
8
13
600
Requirement
300
300
500
500
Find the minimum cost of transportation schedule. Use Vogel's method for finding the
initial basic feasible solution.
[10]
OR
5.
Give the following across city distance table, find the minimum distance root provided
his home town is A.
[10]
To
From
A
B
C
D
E
A
7
6
8
4
B
7
8
5
3
S
C
6
8
9
7
D
8
5
9
8
E
4
6
7
8
6.
Two jobs are to be processed on four machines A, B, C and D. The technological order
for these jobs on machines is as follows:
Job 1
A
B
C
D
Job 2
D
B
A
C
Processing times are given in the following table:
Machines
A
B
C
D
Job 1
4
6
7
3
Job 2
4
7
5
8
Solve it by graphical method.
[10]
OR
7.
A manufacturer is offered two machines A and B. Machine A is priced at Rs.5000 and
its running costs are estimated at Rs.800 for each of the first five years increasing by
Rs.200 per year in the sixth and subsequent years. Machine B that has the same capacity
as A costs Rs.2500 but would have running costs Rs.1200 per year for six years,
increasing by Rs.200 per year thereafter. If money is worth 10% per year, which machine
should be purchased?
[10]
8.
A company has to transport some goods from city A to city J. The cost of transportation
between the different cities is given in the following network. Find the optimal route
connecting cities A and J.
[10]
D
E
F
B
C
B
4
3
-
A
5
4
C
-
2
6
J
G
H
I
G
7
D
3
6
-
H
3
E
5
7
8
I
8
F
-
9
9
OR
9.a)
Explain the terms i) Payoff matrix ii) saddle point iii) value of the game.
b)
Solve the following game graphically where pay off matrix for player A has been
prepared.
8
-6
7
-4
S
-7
6
[5+5]
-4
-2
10.
Beta industry estimates that it will sell 24000 units of its product for the forthcoming
year. The ordering cost is Rs.150 per order and carrying cost per unit per year is 20% of
the purchase price per unit. The purchase price per unit is Rs.50. Find:
a) Economic Order Quantity
b) No. of orders per year
c) Time between successive orders.
Derive the formula for economic ordering quantity by clearly stating the assumptions of
it and use it.
[10]
OR
11.a) Explain about Kendal notations used in queuing theory.
b) 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 service time distribution is also
exponential with an average 36 minutes. Calculate the following:
i) The average number of trains in the queue.
ii) The average waiting of a train in the system.
iii) The probability that the number of trains in the system exceeds 10.
[4+6]
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This post was last modified on 17 March 2023