Hall Ticket No Question Paper Code: CMB011
INSTITUTE OF AERONAUTICAL ENGINEERING
(Autonomous)
MBA III Semester End Examinations (Supplementary) May/June, 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. Define operations research. Discuss the process of operations research.
Explain any five models of operations research in detail.
2. Describe the managerial applications of operations research.
Explain the nature and scope of operations research in detail.
UNIT II
3. A person requires 10, 12 and 12 units chemicals of B and C respectively for his garden. A
liquid product contains 2 and 1 units of A,B and C respectively per jar. A dry product contains
1,2 and 4 units of A,B and C per carton. If the liquid product sells for Rs.3 per jar and the dry
product sells for Rs.2 per carton, how many of each should be purchased, in order to minimize
the cost and meet the requirements?
A product is produced by 4 factories F1, F2, F3 and F4. Their unit production cost are Rs.2,
1 and 5 only. Production capacity of the factories are 50, 70, 40 and 50 units respectively. The
product is supplied to 4 stores S1, S2, S3 and S4. The requirements of which are 25, 35, 105 and
20 respectively. Unit cost of transportation are given below.
S1 S2 S3 S4
F1 2 4 6 11
F2 10 8 7 5
F3 13 3 9 12
F4 4 6 8 3
Find the optimal transportation plan such that total production and transportation cost is minimum.
4. Solve the following LPP by graphical method. Minimize Z 20X1 40X2 Subject to constraints
36X1 6X2 108
3X1 12X2 36
20X1 10X2 100
X1, X2 0
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Write the Dual of the following LPP
Min Z 4X1 5X2- 3X3
Subject to constraints,
X1+ X2 X3 22
3X1+ 5X2 2X3 65
X1+ 7X2 +4X3 120
X1 X2 0 and X3 is unrestricted
UNIT III
5. What are the applications of assignment problem with an algorithm.
Solve the following traveling salesman problem. Salesman has to return to the origin after visiting
all the cities.
From/to A B C D E
A ∞ 4 7 3 4
B 4 ∞ 6 3 4
C 7 6 ∞ 7 5
D 3 3 7 ∞ 7
E 4 4 5 7 ∞
6. Explain the various steps in Hungarian method? How do you solve the unbalanced assignment
problem.
A company has taken the third floor of a multi-storied building for rent with a view to locate
one of their zonal offices. There are five main rooms in this to be assigned to five managers.
Each room has its own advantages and disadvantages. Some have windows, some are closer to
the wash rooms or to the canteen or secretarial pool. The rooms are of all different sizes and
shapes. Each of the five managers were asked to rank their room preference amongst the rooms
301, 302, 303, 304 and 305. Their preferences were recorded in a table as indicated below
M1 M2 M3 M4 M5
302 302 303 302 301
303 304 301 305 302
304 305 304 304 304
301 305 303
302
Most of the managers did not list all the five rooms since they were not satisfied with some
of these rooms and they have left these from the list. Assuming that their preferences can be
quantified by numbers, find out as to which manager should be assigned to which room so that
their total preference ranking is a minimum.
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UNIT IV
7. What is Decision Tree Analysis? Explain the step by step procedure of decision tree analysis.

Explain the different types of Decision-Making Environments with suitable examples
8. Discuss the various steps in decision analysis. Explain how managerial applications help decision
making
What are the ingredients of decision problems.
UNIT V
9. Explain the various characteristics of queuing models.
At a service counter of fast-food joint, the customers arrive at the average interval of six minutes
whereas the counter clerk takes on an average 5 minutes for preparation of bill and delivery of
the item. Calculate the following
i. Counter utilization level
ii. Average waiting time of the customers at the fast food joint
iii. Expected average waiting time in the line
iv. Average number of customers in the service counter area
v. Average number of customer in the line
vi. Probability that the counter clerk is idle
vii. Probability of finding the clerk busy
10. Explain the various applications of Queuing models.
A warehouse has only one loading dock manned by a three person crew. Trucks arrive at the
loading dock at an average rate of 4 trucks per hour and the arrival rate is Poisson distributed.
The loading of a truck takes 10 minutes on an average and can be assumed to be exponentially
distributed . The operating cost of a truck is Rs.20 per hour and the members of the crew are
paid Rs.6 each per hour. Would you advise the truck owner to add another crew of three
persons?
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