This document contains 30 multiple choice and numerical questions related to quantitative techniques in management. The questions are organized into 5 units: (1) Introduction to Operations Research, (2) Linear Programming, (3) Assignment Problem, (4) Sequencing Problem, and (5) Replacement Problem. The questions cover topics such as linear programming, transportation problems, queuing theory, project management, and replacement analysis. Sample questions include formulating linear programming models, solving transportation problems, analyzing queuing systems, and determining optimal replacement times for equipment.

1. BORA INSTITUTE OF MANAGEMENT SCIENCES,
LUCKNOW
MBA
SEMESTER II (SESSION 2018-19)
QUANTITATIVE TECHNIQUES IN MANAGEMENT
(KMB206)
MODEL QUESTIONS
UNIT I
Introduction to Operations Research
1. Operations research is a very powerful tool and analytical process that offers the
presentation of an optimum solution in spite of its limitations. Discuss. (2018)
UNIT II
Linear Programming Problem
2. “Linear programming is one of the most frequently and successfully used operations
research technique to managerial and business decisions.” Elucidate. (2007, 2013)
3. The ABC Company has been a producer of picture tubes for TV sets and certain
printed circuits for radios. The company has just expanded into full scale production
and marketing of AM-FM radios. It has built a new plant that can operate 48 hours per
week. Production of an AM radio in the new plant will require 2 hours and production
of AM-FM radio requires 3 hours. Each AM radio will contribute Rs.40 to profits while
an AM-FM radio will contribute Rs.80 to profits. The marketing department, after
extensive research, has determined that a maximum of 15 AM radios and 10 AM-FM
radios can be sold each week. Formulate a linear programming model to determine the
optimum production mix of AM and AM-FM radios that will maximize profits. Solve
it using the graphical method and the simplex method. (2008)
4. A paper mill produces two grades of paper namely X and Y. Owing to raw material
restrictions, it cannot produce more than 400 tons of grade X and 300 tons of grade Y
in a week. There are 160 production hours in a week. It requires 0.2 hours and 0.4 hours
to produce a ton of products X and Y, respectively with corresponding profits of
Rs.200 and Rs.500 per ton. Formulate the above as an LPP to maximise profit. (2018)
5. Solve the following LPP:
Max. z=5x1+10x2+8x3
subject to
3x1+5x2+2x3≤60
4x1+4x2+4x3≤72
2x1+4x2+5x3≤100
where x1, x2, x3≥0 (2017)
6. Write the dual of the following primal problem:
Maximise: z = -5x1 + 2x2
Subject to the constraints:
x1 - x2 ≥ 2
2x1 + 3x2 ≤ 5
x1, x2 ≥ 0 (2010)

2. 2
RMB207 QUANTITATIVE TECHNIQUES FOR MANAGERS BIMS
Transportation Problem
7. Determine an initial basic feasible solution to the following transportation problem
using Vogel’s approximation method.
Destination 1 Destination 2 Destination 3 Destination 4 Supply
Source 1 21 16 15 3 11
Source 2 17 18 14 23 13
Source 3 32 27 18 41 19
Demand 6 10 12 15
(2018)
8. Goods to be transported from factories A, B, C and D to warehouse X, Y and Z. The
transportation cost per unit, capacities of the factories and requirements of the
warehouses are given in the following table. Find the distribution with minimum cost.
Use the least cost method for finding the initial solution and the stepping stone method
for optimizing it.
Factory
A B C D Requirement
Warehouse
X 15 24 11 12 2000
Y 25 20 14 16 4000
Z 12 16 22 13 7000
Capacity 3000 2500 3500 4000
(2006)
UNIT III
Assignment Problem
9. What is an assignment problem? Give two applications. (2006)
10. Consider an example where four jobs (J1, J2, J3 and J4) need to be executed by four
workers (W1, W2, W3 and W4), one job per worker. The matrix below shows the cost
of assigning a certain worker to a certain job. The objective is to minimise the total cost
of the assignment.
J1 J2 J3 J4
W1 82 83 69 92
W2 77 37 49 92
W3 11 69 5 86
W4 8 9 98 23
(2018)
11. A marketing manager has five salesmen and 5 sales districts. Considering the
capabilities of the salesmen and the nature of districts, the marketing manager estimates
that sales per month (in lakhs of rupees) for each salesman in each district would be as
follows:
District
A B C D E
Salesman
I 32 38 40 28 40
II 40 24 28 21 36
III 41 27 33 30 37
IV 22 38 41 36 36
V 29 33 40 35 39

3. 3
RMB207 QUANTITATIVE TECHNIQUES FOR MANAGERS BIMS
Find the assignment of the salesmen to districts that will result in maximum sales.
(2006)
Game Theory
12. In a game the organizer can hide the prize in one of five foxholes (1, 2, 3, 4 or 5),
alternated with four aiming spots A, B, C and D. A gunner has a single shot and may
fire at any of the four spots A, B, C and D. The gunner will win the prize if it is in a
foxhole adjacent to the spot where the shot was fired. For example, if the gunner fires
at spot B, he/she would win the prize if it is in foxhole 2 or 3.
1 A 2 B 3 C 4 D 5
(a) Assuming this to be a zero-sum game, construct the reward matrix.
(b) Find and eliminate all dominated strategies.
(c) Write down each player’s LP.
(d) Find the optimal strategy and value of the game. (2010)
13. Reduce the following two person zero-sum game to 2×2 orders and obtain the optimal
strategies for each player and the value of the game:
Player B
B1 B2 B3 B4
Player A
A1 3 2 4 0
A2 3 4 2 4
A3 4 2 4 0
A4 0 4 0 8
(2018)
14. Firms X and Y are competing for a business. Whatever X gains, Y loses. The matrix
shows the utility to firm X for various market share
Firm X’s Utility
Y
No advertising Medium advertising Heavy advertising
X
No advertising 60 50 40
Medium advertising 70 70 50
Heavy advertising 80 60 75
Find the optimal strategies for firm X and Y and also the value of the game. (2018)
UNIT IV
Sequencing Problem
15. What is a sequencing problem? Explain how to process n jobs through m machines.
(2018, 2005)
16. There are five jobs, each of which are to be processed on 3 machines A, B and C in the
order ABC. Processing times are:
Job A B C
1 4 5 8
2 9 6 10
3 8 2 6
4 6 3 7
5 5 4 11
Determine the sequence for the five jobs that will minimise the elapsed time T. (2005)

4. 4
RMB207 QUANTITATIVE TECHNIQUES FOR MANAGERS BIMS
17. Use the graphical method to minimize the time needed to process the following jobs
on the machine shown. Also calculate the total elapsed time to complete both jobs.
Machine
Job 1 Sequence A B C D E
Time (hrs.) 3 4 2 6 2
Machine
Job 2 Sequence B C A D E
Time (hrs.) 5 4 3 2 6
(2010)
18. Two jobs, A and B are to be processed on 6 machines. The sequence of machines and
the processing times are given in the following table:
Job A Machine sequence M1 M2 M3 M4 M5 M6
Time (hours) 6 4 5 3 4 2
Job B Machine sequence M1 M2 M3 M4 M5 M6
Time (hours) 4 8 4 3 6 4
What is the minimum time in which both the jobs can be completed? (2018)
Queuing Theory
19. Specify the characteristics of M/M/I queue model. (2018, 2008, 2005)
20. A foreign MNC bank is considering opening a drive-in-window for customer service.
Management estimates that customers will arrive for service at the rate of 12 per hour.
The teller, whom it is considering to staff the window can serve customers at the rate
of one every three minutes. Assume Poisson arrivals and exponential service, find:
(i) Utilization of the teller;
(ii) Average number in the system;
(iii) Average waiting time in the line; and
(iv) Average waiting time in the system. (2013)
21. A self-service store employs one cashier at its counter. Nine customers arrive on an
average of every 5 minutes, while the cashier can serve 10 customers in 5 minutes.
Assuming Poisson distribution for arrival rate and exponential distribution for service
rate, find:
(i) Average number of customers in the system.
(ii) Average number of customers on queue or average queue length.
(iii) Average time a customer spends in the system.
(iv) Average time a customer waits before being served. (2018)
22. Customers arrive at the first-class ticket counter of a theatre at the rate of 12 per hour.
There is one clerk serving the customers at the rate of 30 per hour. What is the
probability that
(i) there is no customer on the counter;
(ii) there are more than two customers in the system;
(iii) there is no customer waiting to be served;
(iv) a customer is being served and nobody is waiting? (2011)
UNIT V
Replacement Problem
23. Explain the costs which are relevant to decisions for replacement of depreciable assets.
(2010)

5. 5
RMB207 QUANTITATIVE TECHNIQUES FOR MANAGERS BIMS
24. The purchase price of a machine is Rs.52000. The installation charges amount to
Rs.14400 and its scrap value is only Rs.6400. The maintenance cost in various years is
given below:
Year: 1 2 3 4 5 6 7 8
Maintenance Cost: 1000 3000 4000 6000 8400 11600 16000 19200
After how many years should the machine be replaced? Assume that the machine
replacement can be done only at year-end. (2011)
25. XYZ manufacturing company is using a machine whose purchase price is Rs.65000.
The installation charges amount to Rs.18000 and the machine has a scrap value of only
Rs.8000 because the firm has a monopoly of this type of work. The maintenance cost
in various years is given in the following table:
Year: 1 2 3 4 5 6 7 8 9
Maintenance
Cost (Rs.)
1250 3750 5000 7500 10500 14500 20000 24000 30000
Determine after how many years the machine should be replaced, assuming that the
machine replacement can be done only at year-end. (2008)
Project Management
26. Distinguish between PERT and CPM. Also explain the meaning of “crashing of
networks” and state its usefulness in business decision making. (2018, 2007, 2005)
27. A project is composed of nine activities whose time estimates are as given below:
Activity 1-2 1-3 1-4 2-5 3-5 4-6 5-6 6-7 5-7
Optimistic 1 3 2 1 3 2 4 6 3
Most likely 1 5 2 11 6 5 6 8 7
Pessimistic 7 7 8 15 9 8 14 10 11
Draw the project network and trace all the possible paths from it. What is the expected
project length? (2005)
28. For a small project of 12 activities, the details are given below. Draw a network and
compute the earliest occurrence time, latest occurrence time, critical activities and
project completion times:
Activity: A B C D E F G H I J K L
Dependence: - - - B, C A C E E D, F, H E I, J G
Duration (days): 9 4 7 8 7 5 10 8 6 9 10 2
(2018)
29. Draw a network diagram on the basis of the following data:
Activity 1-2 1-4 1-7 2-3 3-6 4-5 4-8 5-6 6-9 7-8 8-9 9-10
Duration (days) 2 2 1 4 1 5 8 4 3 3 5 2
Find the critical path, total duration and slack time. (2007)

6. 6
RMB207 QUANTITATIVE TECHNIQUES FOR MANAGERS BIMS
30. The owner of a chain of fast food restaurants is considering a new computer system
for accounting and inventory control. A computer company sent the following
information about the system installation:
Activity
Identification
Immediate
Predecessor
Time
Most optimistic Most likely Most pessimistic
A - 4 6 8
B A 5 7 15
C A 4 8 12
D B 15 20 25
E B 10 18 26
F C 8 9 16
G E 4 8 12
H D, F 1 2 3
I G, H 6 7 8
(i) Construct arrow diagram.
(ii) Find critical path and expected project completion time.
(iii) Find probability of completing project in 55 days. (2018)