Register Number :
Name of the Candidate :
5256
B.Sc. DEGREE EXAMINATION, 2012
( MATHEMATICS )
( THIRD YEAR )
( PART - III )
( PAPER - VII )
740. OPERATIONS RESEARCH
( Including Lateral Entry )
May ] [ Time : 3 Hours
Maximum : 75 Marks
Calculator can be used.
Answer any FIVE questions.
ALL questions carry equal marks.
(5 × 20 =100)
1. (a) Television company operates two assembly
lines, Line-I and Line-II. Each line is used
to assemble the components of three types
of televisions:
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9. A manufacturer is offered two machines A and
B. A is priced at 5,000 and running costs
are estimated at 800 for each of the first five
years, increasing by 200 per year in the sixth
and subsequent years. Machine – B, which has
the same capacity as A, cost 2,500 but will
have running costs of 1,200 per year for six
years, increasing by 200 per year thereafter.
If money is worth 10% per year, which machine
should be purchased?
10. (a) Define
(i) Failure rate.
(ii) Instantaneous failure rate.
(b) An electronic circuit consists of 15 valves,
20 resistors and 10 capacitors all
connected in a series. The components in
each category are identical and their failure
times are found to follow exponential
distribution with the following mean failure
times :
Values Resistors Capacitors
Mean failure
time (hrs.) 10,000 20,000 20,000
What is the mean time between failure of the
system? What is its reliability for 100 hours?
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Colour, Standard and Economy. The
expected daily production on each line is
as follows:
TV model Line-I Line-II
Colour 3 1
Standard 1 1
Economy 2 6
The daily running costs for two lines
average 6,000 for line-I and 4,000
for Line-II . It is given that the company
must produce at least 24 colour, 16
standard and 48 Economy TV sets for
which an order is pending.
Formulate the above problem as an LPP.
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8. (a) Discuss various costs associated with
inventory.
(b) A dealer supplied you the following
information with regard to a product dealt
in by him :
Annual demand : 10,000 units;
Ordering cost : 10 per order
Price : 20 per unit.
Inventory carrying cost : 20% of the
value of inventory per year.
The dealer is considering the possibility of
allowing some back-order (stock out) to occur.
He has estimated that the annual cost of backordering
will be 25% of the value of money.
(i) What should be the optimum number of
units of the product he should buy in one
lot?
(ii) What quantity of the product should he
allowed to be back-ordered if any?
(iii) What would be the maximum quantity of
inventory at any time of the year?
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7
3. Use two-phase simplex method to maximize
Z = 5x1 + 3x2
subject to the constraints
2x1 + x2 1
x1 + 4x2 6
and x1, x2 0
4. (a) Write the dual of the LPP:
Minimize Z = 4x1 + 6x2 + 18x3
subject to the constraints
x1 + 3x2 3
x1 + 2x3 5
and x1, x2, x3 0.
(b) Use dual simplex method to solve the
following problem:
Minimize Z = 10x1 + 6x2 + 2x3
subject to the constraints
–x1 + x2 + x3 
3x1 + x2 – x3 2
5. (a) Explain Vogel’s approximation method to
solve transportation problem for an initial
solution.
(b) Consider a transportation problem with
m = 3 and n = 4, where
C11 = 2 C12 = 3 C13 = 11 C14= 7
C21 = 1 C22 = 0 C23 = 6 C24= 1
C31 = 5 C32 = 8 C33 = 15 C34= 9
Suppose S1 = 6, S2 = 1 and S3 = 10
whereas D1 = 7, D2 = 5, D3 = 3 and
D4 = 2, obtain an optimum solution for
the TP.
6. Four professors are each capable to teaching
any one of four different courses. Class
preparation time in hours for different topics
varies from professor to professor and its given
in the table below. Each professor is assigned
only one course. Determine an assignment
schedule so as to minimize the total course
preparation time for all courses.
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45
Pro- Linear Queuing Dynamic Regression
fessor Programm- theory Programm- Analysis
ing ing
A 2 10 9 7
B 15 4 14 8
C 13 14 16 11
D 4 15 13 9
7. Determine the optimal sequence of jobs that
minimizes the total elapsed time based on the
following information processing time on
machines is given in hours and passing is not
allowed.
Job A B C D E F G
Machine-M1 3 8 7 4 9 8 7
Machine-M2 4 3 2 5 1 4 3
Machine-M3 6 7 5 11 5 6 12
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(b) Using graph, find the maximum value of
Z = 5x1 + 3x2
subject to the constraints
3x1 + 5x2 15
5x1 + 2x2 10
x1, x2 0.
2. (b) Find all the basic feasible solutions of the
equations.
2x1 + 6x2 + 2x3 + x4 = 3.
6x1 + 4x2 + 4x3 + 6x4 = 2.
(b) Use simplex method of solve the following
LPP:
Maximize Z = x1 – x2 + 3x2
subject to the constraints
x1 + x2 + x3 10
2x1 – x3 2
2x1 – 2x2 + 3x3 0
x1 , x2 , x3 0
3
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