1
Seat No.: Enrolment
GUJARAT TECHNOLOGICAL UNIVERSITY
MCA SEMESTER- IV • EXAMINATION SUMMER 2014
Subject Code:640003 Date:03/06/2017
Subject Name: Operation Research
Time: 10.30 AM TO 01.00 PM Total Marks: 70
Instructions:
1. Attempt all questions.
2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.
Q.1

Define:
Infeasible Solution Unbounded Solution
Explain types of events with reference of PERT/CPM.
04
03

Discuss Monte Carlo Simulation Method.
07
Q.2

Define: Two-Person Zero Sum Game with example
For what value of the game with following pay-off matrix is strictly determinable?
Player B
Player A
B1
B2
B3
A1
Y
6
2
A2

Y

A3

4
Y
02
05

Solve following LPP using Simplex Method:
Max Z a 4b 5c
Subject to,
3a 3b 22, a 2b 3c 14, 3a 2b 14
And c 0
07
OR

Write dual of following LPP:
Min Z x y z
Subject to,
x 3y 4z x 2y 2y z 4
And y z is unrestricted
07
Q.3

Customers arrive at a box office window, being manned by a single individual, according to a Poisson input process with a mean rate of 30 per hour. The time required to serve a customer has an exponential distribution with a mean of 90 seconds.
i. Find expected number of customers in a system.
ii. Find queue length.
07
2

Solve following assignment problem:
Jobs
Worker
A
B
C
D
1
45
40
51
67
2
57
42
63
55
3
49
52
48
64
4
41
45
60
55
07
OR
Q.3

Find initial feasible solution for given transportation problem using VAM:
Distribution Centre
Supply
Plant
D1
D2
D3
D4
P1
20
30
110
70
6
P2
10
0
60
10
1
P3
50
80
150
90
10
Demand
7
5
3
2
07

Define: Queue Discuss dynamic queue discipline in detail.
07
Q.4

Draw a network diagrams for the following:
ii)
Activity
Predecessor
Activity
A

B

C

D
A
E
B
F
C
G
F
H
F
Activity
Predecessor
Activity
A

B

C

D
A
E
B
F
C
G
F
H
F
07

A manufacturer has to supply his customer with 600 units of his product per year. Shortages are not allowed and the storage cost amounts to Rs. 0.60 per unit per year. The set-up cost per run is Rs. 80. Find the optimum run size, the minimum average yearly cost and optimum order cycle time.
07
OR
Q.4

A pipeline is due for repairs. The repair would cost Rs. 10,000 and would last for three years. Alternatively, a new pipeline can be laid at a cost of Rs. 30,000, which would for 10 years. Assuming the cost of capital to be 10% and ignore salvage value, which alternative should be adopted?
07

Use the graphical method to minimize the time needed to process the following jobs on the machines shown, i.e. for each machine find the job that should be done first. Also, calculate the total elapsed time to complete both jobs.
Job 1
Machines
Sequence:
A
B
C
D
E
Time(Hrs.)
3
4
2
6
2
Job 2
Machines
Sequence:
B
C
A
D
E
Time(Hrs.)
5
4
3
2
6
07
3
Q.5

Discuss errors and dummies in network with suitable example.
07

What is rim condition? Write explain general mathematical model of transportation problem.
07
OR
Q.5

An aircraft company uses rivets at a constant rate of 2500 per year. Each unit costs Rs. 30. The company personnel estimate that it costs Rs. 130 to place an order, and that the carrying cost of inventory is 10% per year. How many numbers of orders be placed for the time period? Determine the optimum size of each order.
07

Solve given transportation problem using LCM:
Destination
Supply
Source
D1
D2
D3
D4
S1
11
13
17
14
250
S2
16
18
14
10
300
S3
21
24
13
10
400
Demand
200
225
275
250
07