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Reg
APJ ABDUL KALAM TECHNOLOGICAL UNIVERSITY
SECOND SEMESTER MCA DEGREE EXAMINATION, APRIL 2018
Course Code: RLMCA 108
Course Name: OPERATIONS RESEARCH
Max. Marks: 60 Duration: 3 Hours
PART A
Answer all questions, each carries 3 marks. Marks
1 Explain the use of artificial variables in solving a linear programming problem
2 What is meant by duality in linear programming problems. Write the
fundamental principle of duality

3 Describe the Matrix Minima method.
4 Explain Saddle point Two person zero sum game
5 Explain single server Poisson queuing model with infinite capacity.
6 Explain pure birth and death process
7 What you mean by simulation? Explain.
8 Write the steps for generating random numbers.
PART B
Each question carries 6 marks.
9 A company produces two articles A and B. There are two different
departments through which the articles are processed such as assembly and
finishing. The potential capacity of the assembly department is 60 hours per
week and that of the finishing department is 48 hour per week. The
production of one unit of A requires 4 hours in assembly and 2 hours in
finishing. Each of the unit B requires 2 hours in assembly and 4 hours in
finishing. If profits in Rs. 8 for each unit of A and Rs. 6 for each unit of
find out the number of units of A and B to be produced each week to get the
maximum profit. Use graphical method.

OR
Solve the following LPP
Maximise Z x1+x2+x3
Subject to 4x1+5x2+3x3
10x1+7x2+x3 12; x1, x2, x3 0

10 Write the dual of the following LPP
Maximise Z x1+x2+x3
Subject to 4x1+5x2+3x3 15
10x1+7x2+x3 12; x1, x2, x3 0

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State the complementary slackness theorem.
OR
Using dual simplex method solve the following LPP,
Minimise Z 3x1+x2
Subject to x1+x2
2x1+3x2 2 x1,x2

11 Solve the following transportation problem,
Warehouses
W1 W2 W3 Supply
F1 16 20 12 200
Factories F2 14 8 18 160
F3 26 24 16 90
Demand 180 120 150

OR
Solve the following Assignment problem,
1 2 3 4
A 10 12 19 11
B 5 10 7 8
C 12 14 13 11
D 8 15 11 9

12 Solve the following 2x4 game graphically,
Player B
B1 B2 B3 B4
Player A A1 2 1 0
A2 1 0 3 2

OR
Solve the following game using dominance property.
Player B
B1 B2 B3 B4
Player A A1 3 2 2 0
A2 3 4 2 4
A3 4 5 4 0
A4 0 1 0

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13 What are the elements of a queuing system? What are the fundamental
characteristics of a queueing system?

OR
At a one man barber shop, customers arrive according to poisson
distribution with a mean arrival rate of 5 per hour and his hair cutting time
was exponentially distributed with an average hair cut time being 10
minutes. It is assumed that because of his excellent reputation customers
were always willing to wait. Calculate the following
Average number of customers in the shop and the average number of
customers waiting for haircut.
The average number of customers who have to wait prior to getting into
barber's chair.
The percentage of time, an arrival can walk right in, without having to
wait.

14 Explain Monte-Carlo simulation.
OR
Customers arrive at a milk booth for the required service. Assume that inter
arrival and service times are constant and given by 1.8 and 4 time units,
respectively. Simulate the system by hand computations for 14 time units.
What is the average waiting time per customer? What is the percentage idle
time of the facility? (Assume that the system starts at t 0