DISTANCE EDUCATION
M.B.A. (H.R.M.) DEGREE EXAMINATION, MAY 2017.
First Semester
QUANTITATIVE METHODS
(Upto 2012-13 Academic Year and 2013 Calendar Year)
Time Three hours Maximum 100 marks
SECTION A — 8 40 marks)
Answer any FIVE questions.
All questions carry equal marks.
1. Discuss the steps involved in formulation of Linear
Programming Problems.
Solve graphically;
Minimize Z 6x1 4x2 60
Subject to
0
2 18
3 7 84
5 4 60
1 2
1 2
1 2
1 2




x x
x x
x x
x x
2. A company is manufacturing two products x and y by
using two types of raw materials A and B. The
requirement of materials for producing one unit of each
product is as follows:
Product Material A Material B
X 2 units 3 units
Y 4 units 2 units
Sub. Code
14
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At present, only 80 units of material A and 60 units of
material B are available. If the profit for product x is the
Rs. 60 per unit, and it is Rs. 50 per product y. What
should be the product mix to earn maximum profit?
Determine graphically as well as using the simplex
method.
3. Define the following and indicate their significance to
decision-making with linear programming and the
simplex method.
Pivot Column
Pivot row
Degeneracy
Multiple optima.
4. Write the key features of conditional probabilities.
A bag contains 30 balls numbered from 1 to 30. One
ball is drawn at random. Find the probability that
the number of the drawn will be a multiple of 5
or and 3 or 7.
5. What are the types of decisions? Explain them in
brief with suitable examples.
Consider the details of two competing alternatives
as shown in the following table. The initial outlay of
each of the alternatives is Rs. 50,000,000. The life of
each alternative is 15 years. Find the best
alternative when the interest rate is using the
expected value creation.
Alternative 1 Alternative 2
Annual Revenue

Probability Annual Revenue

Probability
12,00,000 0.25 22,00,000 0.20
19,00,000 0.45 24,00,000 0.45
28,00,000 0.30 32,00,000 0.35
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6. A small retailer has studied the weekly receipts and
payments over the past 200 weeks and has developed the
following set of information;
Weekly Receipts Probability Weekly Payments Probability
3000 0.20 4000 0.30
5000 0.30 6000 0.40
7000 0.40 8000 0.20
12000 0.10 10000 0.10
Using the following set of random numbers, simulate the
weekly pattern of receipts and payments for the 12 weeks
of the next quarter, assuming further that the beginning
bank balance is Rs. 8,000. what is the estimated balance
at the end of the 12 weekly period? What is the highest
weekly balance during the quarter? What is the average
weekly balance for the quarter?
Random Numbers:
For Receipts 03 91 38 55 17 46 32
For Payments 61 96 30 32 03 88 48
For Receipts 43 69 72 24 22
For Payments 28 88 18 71 99
7. Evening shift resident doctors in the Healthy Hospital
work five consecutive days and have two consecutive days
off. Their five days work can start on any day of the week
and the schedule rotates indefinitely. The hospital
requires the following minimum number of doctors
working:
S M T W T F S
35 55 60 50 60 50 45
No more than 40 doctors can start their five working days
on the same day. Formulate a general linear
programming model to minimize the number of doctors
employed by the hospital.
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8. What is investment analysis? Why is it of great
significance to a firm?
MNV Electronics is engaged in producing a certain
component which is sold at a uniform price of Rs. 8
each. The variable cost of producing the component
amounts to Rs. 4.80 per unit while the fixed costs
amount to Rs. 24,000. How many units of the
component must be produced and sold so that the
company breaks even? How much sales would be
made at this level of activity?
SECTION B — 15 60 marks)
Answer any FOUR questions.
All questions carry equal marks.
9. The Marketing Department of Everest Company has
collected information on the problem of advertising on the
problem of advertising for its products. This relates to the
advertising media available, the number of families
expected to be reached with each alternative, cost per
advertisement, the maximum availability of each medium
and the expected exposure of each one (measured as the
relative value of one advertisement in each of the media).
The information is as given here;
Advertising
Media
No. of
Families
Expected
to cover
Cost
Per
Ad

Maximum
Availability
(No. of times)
Expected
Exposure
(Units)
TV (30 sec) 3000 8000 8 80
Radio (15
sec)
7000 3000 30 20
Sunday
Edition of
Daily
page)
5000 4000 4 50
Magazine
Page)
2000 3000 2 60
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Other information and requirement:
The advertising budget is Rs.
At least 40,000 families should be covered. (The
families receiving messages could be common. But a
family receiving three messages, for example, would
be taken to be equivalent to three).
At least 2 insertions are given in Sunday edition of
Daily but not more than 4 ads should be given on the
TV.
Draft this as a Linear Programming Problem. The
company's objective is to maximize the expected
exposure.
10. What is linear programming? What are its major
merits and limitations?
A company manufactures two products A and B.
Product A yields contribution of Rs. 30 per unit and
product B Rs. 40 per unit towards profits and fixed
costs. It is estimated that the sales of product A for
the coming month will not exceed 20. Sales of product
B have not been estimated but the company does
have a contract to supply at least 10 units to a
regular customer.
Machine hours available for the coming month are
100 and products A and B require 4 hours and 2
hours respectively to produce one unit. Labour hours
available are 180 and products A and B require 4 and
6 hours of labour respectively. Materials available
are restricted to 40 units and the two products each
use one unit of material per unit. Determine the
optimal product mix.
11. A company has five warehouse and five stores. The
warehouses have a total surplus of 430 units of a given
commodity that is divided among them as follows;
Warehouse W1 W2 W3 W4
Surplus 150 30 120 130
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The five stores have, in all, a requirement of 450 units of
the commodity, individual requirement are;
Store S1 S2 S3 S4 S5
Requirement 80 60 20 210 80
Cost of shipping one unit from the warehouse to the store
is displayed in the following table:
Warehouse Store
S1 S2 S3 S4 S5
W1 9 12 10 10 6
W2 5 18 12 11 2
W3 10 M 7 3 20
W4 5 6 2 M 8
M in the table indicates that the route is not available.
How should the company arrange to transport the units
so that the transportation cost is minimized?
12. A small retailer has studied the weekly receipts and
payments over the past 200 weeks and has developed the
following set of information:
Weekly Receipts Probability Weekly Payments Probability
3000 0.20 4000 0.30
5000 0.30 6000 0.40
7000 0.40 8000 0.20
12000 0.10 10000 0.10
Using the following set of random numbers, simulate the
weekly pattern of receipts and payments for the 12 weeks
of the next quarter, assuming further that the beginning
bank balance is Rs. 8000. What is the estimated balance
at the end of the 12 weekly periods? What is the highest
weekly balance during the quarter? What is the average
weekly balance for the quarter?
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13. The manager of a book store has to decide the number of
copies of a particular tax law book to order. A book costs
Rs. 60 and is sold for Rs. 80. Since some of the tax laws
change year after year, any copies unsold while the
edition is current must be sold for Rs. 30. From past
records, the distribution of demand for this book has been
obtained as follows;
Demand (No. of copies) 15 16 17 18 19 20 21 22
Proportion 0.05 0.08 0.20 0.45 0.10 0.07 0.03 0.02
14. What are pay-off and regret functions? How can
entries in a regret table be derived from a pay-off
table?
Explain the posterior analysis of decision-making.
Define the expected value of sample information.
15. Discuss the methods of finding initial feasible
solution of a transportation problem and state the
advantages, limitations and two areas of application
for each of them.
Give a schematic of solving a transportation
problem.