B.Voc. DEGREE EXAMINATION, APRIL 2016
Second Semester
Software Development
Allied II — MATHEMATICS OPTIMIZATION
TECHNIQUES
(2014 onwards)
Time 3 Hours Maximum 75 Marks
Part A (10 2 20)
Answer all questions.
1. Define Optimization Techniques.
2. Define slack variable.
3. What does VAM stand for?
4. What is the use of Graphical method?
5. What is Balking?
6. Give the formula for finding the traffic intensity of a
single server model.
7. What does CPM stand for?
8. Define optimistic time.
9. Define a sequencing problem.
10. Define total elapsed time.
Sub. Code
5SD2A1
RW-10876
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Part B 5 25)
Answer all questions, choosing either or
11. Explain the advantages of optimization techniques.
Or
Write the dual of the following LPP
Max Z 3x1 5x2 2x3
Subject to
unrestricted in sign.
2 5
4
1 3 2
1 3
1 2 3
x x x
x x
x x x



12. Solve the following LPP using graphical method
Min Z 20x1 40x2
Subject to
0.
20 10 100
3 12 36
36 6 108
1 2
1 2
1 2
1 2




x x
x x
x x
x x
Or
Solve the following assignment problem for
minimization
Men
Tasks
E F G H
A 18 26 17 11
B 13 28 14 26
C 38 19 18 15
D 19 26 24 10
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13. Explain the various queue disciplines with
examples.
Or
Explain the applications of queueing systems.
14. Bring out the fundamental difference between CPM
and PERT.
Or
Explain the procedure for finding the critical path
in a PERT network.
15. Explain the steps in the optimum sequence
algorithm.
Or
Explain the applications of job sequencing.
Part C 10 30)
Answer any three questions.
16. Use Dual Simplex method to solve the following LPP
Minimize Z x1 x2
Subject to
0.
7 7
2 4
1 2
1 2
1 2



x x
x x
x x
17. Solve the following transportation problem for
minimization
D1 D2 D3 D4 Supply
S1 3 7 6 4 5
S2 2 4 3 2 2
S3 4 3 8 5 3
Demand 3 3 2 2
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18. A T.V. repairman finds that the time spent on his jobs
has an exponential distribution with mean 30 minutes.
If he repairs sets in the order in which they come in, and
if the arrival of sets in approximately Poisson with an
average rate of 10 per 8 hour day, what is the
repairman's expected idle time each day? How many jobs
are ahead of the average set just brought in?
19. A small project is composed of seven activities, whose
time estimates are given below
Activity 1-2 1-3 1-4 2-5 3-5 4-6 5-6
Optimistic 1 1 2 1 2 2 3
Most likely 1 4 2 1 5 5 6
Pessimistic 7 7 8 1 14 8 15
Draw the project network
Find the expected duration and variance of each
activity
Determine the critical path and the expected project
length.
20. In a factory, there are six jobs to perform, each of which
should go through two machines A and B in the order
B. The processing timing (in hours) for the jobs are
given here. You are required to determine the sequence
for performing the jobs that would minimize the total
elapsed time T. What is the value of
Job J1 J2 J3 J4 J5 J6
Machine A 1 3 8 5 6 3
Machine B 5 6 3 2 2 10