Hall Ticket No Question Paper Code: CMB011
INSTITUTE OF AERONAUTICAL ENGINEERING
(Autonomous)
MBA III Semester End Examinations (Regular) November, 2018
Regulation: IARE-R16
Quantitative Analysis for Business Decisions
Time: 3 Hours Max Marks: 70
Answer ONE Question from each Unit
All Questions Carry Equal Marks
All parts of the question must be answered in one place only
UNIT I
1. Describe important features of Operation Research.
State and explain classification of different models available in practice of Operations Research.

2. Describe important phases of Operations Research.
Discuss in brief various applications and scope of Operations Research in business scenario.[7M]
UNIT II
3. The LPP model with an objective function of Max Z=40X1+35X2 has a feasible region covered
by OABC points in graphical method. Find the value of X1, X2 and Maximum Z. The following
are the ordinates of points and If the Objective is to minimise
what is change in values of X1, X2 and Min Z.
From the following simplex table find whether the solution is leading to an optimal solution?

Table 1
Cj 2 4 0 0
Basis X1 X2 S1 S2 R1 R2 bJ
0 S1 0 0 1 3/4 1/4 2
2 X1 1 0 0 1/2 2
4 X2 0 1 0 1/4 3/4 12
Max
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4. Find the non-degenerate initial solution by Vogel's Approximation Method to the following transportation
problem shown in Table 2.
Table 2
Factory/ Warehouse W1 W2 W3 W4 Supply
A 4 5 2 5 120
B 3 8 4 8 80
C 7 4 7 4 200
Demand 60 50 140 50
Is the following Table 3 initial solution optimal? Check using MODI method.
Table 3
From/ To W1 W2 W3 W4 Slack/Dummy Supply
A 4 5 2(120) 5 0 120
B 8 4 8 80
C 7 200
Demand 60 50 140 50 100
UNIT III
5. Describe the steps followed in solving an Assignment model by Hungarian method.
Find the optimal solution to assignment problem shown in Table 4 value are given in minutes.

Table 4
Men Work A B C D
W1 45 40 51 67
W2 55 40 61 53
W3 49 52 48 64
W4 41 45 60 55
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6. Describe how a travelling salesman model is different from assignment model.
Find the optimal route to the following travelling salesman shown in Table 5. model
Table 5
A B C D
A X 4 7 3
B 4 X 6 3
C 7 6 X 7
D 3 3 7 X
UNIT IV
7. Describe the criterion of optimism and criterion of pessimism with an example.
Solve the following Table 6 using Min-Max regret criterion values given in Lakhs.
Table 6
Nature Strategies N1 N2 N3
S1 7 3 1.5
S2 5 4.5 0
S3 3 3 3
8. Differentiate payoff matrix and decision tree? Is there any benefit in representing a decision problem
in either of these forms? Under what circumstances is a decision tree a better representation
than a decision problem.
The following information available related to a goods transport system shown in Table 7. Lorries
have fixed cost of Rs. per day and variable cost of Rs.200. If the lorry owner has 4 vehicles,
what are its daily expectations? If it is start new business without any Lorries how many Lorries
he has to buy?
Table 7
Number of lorry demand 0 1 2 3 4
Probability 0.1 0.2 0.3 0.2 0.2
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UNIT V
9. Describe the general structure of queuing system with an example.
Arrivals at telephone booth are considered to be Poisson with an average time of 10 minutes
between one arrival and next. The length of phone call is assumed to be exponentially distributed
with a mean time of 3 minutes.
i. What is the probability that a person arriving at the booth will have to wait?
ii. What is the average length of queue?
iii. What is the expected number of customers in the system?
iv. If the waiting time in the queue is 3 minutes for what increase in arrival pattern then a
second counter is installed?
10. Describe the various service process in queuing theory followed in practice with an example.

In machine maintenance, a mechanic repairs four machines. The mean time between service
requirement is 5 hours for each machine and forms an exponential distribution. The men repair
time is one hour and also follows the same distribution pattern. Machine down time cost Rs.
per hour and the mechanic costs is Rs per day of 8 hours.
i. Find the expected number of operating machines.
ii. Determine expected down time cost per day
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