1
Seat No.: Enrolment
GUJARAT TECHNOLOGICAL UNIVERSITY
MCA SEMESTER-IV • EXAMINATION SUMMER 2017
Subject Code: 3640009 Date:06/06/2017
Subject Name: Operations 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 Use graphical method to solve following LPP:
1 2
1 2
1 2
1 2
1 2
6 14
. 5 4 60;
3 7 84;
2 18
0
Minimize Z x x
Sub to x x
x x
x x
x x





07
Construct dual of the following problem
1 2 3
1 2 3
1 3
1 2 3
3 5 7
3 5 7 60
6 40
0
Maximize Z x x x
Subject to x x x
x x
x x x




In context of game theory define Pure and mixed strategies Saddle
Point.
03
04
Q.2 Solve the following LPP using Big-M method
1 2 3
1 2 3
1 2 3
1 2 3
1 2 3
2 3 4
3 4 600
2 4 2 480
2 3 3 540
0
Maximize Z x x x
Subject to x x x
x x x
x x x
x x x





07
What is Simulation? What are the advantages and disadvantages of
Simulation?
For the game with payoff matrix:
Player A
Player B
B1 B2 B3 B4
A1 3 0 6
A2 1 2
A3 5 4 2 3
Determine the best strategies for players A and B and the value of the game. Is this
game fair? strictly determinable?
04
03
OR
Define Operation Research. Explain the features and application areas of
operations research.
07
Q.3 Solve the following Transportation Problem using VAM and obtain an optimal
solution to minimize the cost:
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2
Factory
Warehouse
A
B
C
D
Capacity
1
6
3
5
4
22
2
5
9
2
7
15
3
5
7
8
6
8
Requirement
7
12
17
9

Solve the following Assignment problem.
Operators
Machines
A
B
C
D
1
10
5
7
8
2
11
4
9
10
3
8
4
9
7
4
7
5
6
4
5
8
9
7
5
07
OR
Q.3

Explain what are looping, dangling, burst events, merge events, and dummy activities. Why do we need dummy activities?
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Five men are available to do 5 different jobs from past records. The time (in hours) that each man takes to do each job is known and given in the following table.
Men
Jobs
1
2
3
4
5
A
2
9
2
7
1
B
6
8
7
6
1
C
4
6
5
3
1
D
4
2
7
3
1
E
5
3
9
5
1
Find the assignment of men to jobs to minimize the total time taken.
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Q.4

The data collected in running a machine, the cost of which is Rs. 50,000 are given below:
Year
1
2
3
4
5
6
Operating cost
7500
8000
8500
9000
10000
12250
Resale value
45000
40500
37500
36000
34500
33250
Determine the optimum period of replacement of the machine.
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A purchase manager places order each time for a lot of 500 units of a particular item. From the data, the following results are obtained:
Inventory carrying cost Ordering cost per order Rs. 600
Cost per unit Rs. 50, Annual demand 1000 units
Find out the loss to the organization due to his ordering policy.
07
OR
Q.4

An electric generator costs Rs. 60,000, operating and maintenance costs are Rs. 10,000 per year for the first five years. In the sixth year and subsequent yeas these costs increase by Rs. 3000 per year. Assuming 10% cost of money per year, find the optimum length of time to keep the machine before replacing it.
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Describe the major cost categories used in inventory analysis and their functional relationship to each other.
07
Q.5

Briefly explain the structure of Queuing system.
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Find the sequence for the following eight jobs, that will minimize the total elapsed time for the completion of all the jobs. Each job is processed in the same order CAB. Entries give the time in hours on the machines.
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3
Machines
Jobs
1
2
3
4
5
6
7
8
A
4
6
7
4
5
3
6
2
B
8
10
7
8
11
8
9
13
C
5
6
2
3
4
9
15
11
OR
Q.5

Arrivals at a telephone booth are considered to be Poisson, with an average time of 10 minutes between one arrival and the next. The length of a phone call is assumed to be distributed exponentially, with mean 3 minutes. Find:
1. The probability that an arrival finds that four persons are waiting for their turn.
2. The average number of persons waiting and making telephone calls.
3. The average length of the queue that is formed time to time.
4. The probability that a waiting time of a person in queue shall be more than 2 minutes?
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The precedence relationships of the activities, and activity time estimates (in weeks) of a project is as follows:
Task
A
B
C
D
E
F
G
H
I
J
K
Precedence

A
B
C
B
E
F
E
H
I
J
Time
13
8
10
9
11
10
8
6
7
14
18
1. Draw the network of the project.
2. Find Critical path and critical activities and expected completion time.
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