B.Voc. DEGREE EXAMINATION, NOVEMBER 2015.
Software Development
MATHEMATICS II OPTIMIZATION TECHNIQUES
(2014 onwards)
Time 3 Hours Maximum 75 Marks
Part A (10 2 20)
Answer all questions.
1. State any two advantages of linear programming.
2. Define feasible solution.
3. State any three methods for finding the initial solution to
a transportation problem.
4. How many basic variables will be there in a
transportation problem?
5. What is reneging?
6. List the various queueing disciplines.
7. What does PERT stand for?
8. Give the formula for finding the expected time-tocompletion
of an activity in a PERT network.
9. Explain any one application of job sequencing.
10. Define idle time.
Sub. Code
4SD2A1
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Part B 5 25)
Answer all questions, choosing either or
11. Explain the applications of optimization techniques.
Or
Write the dual of the following LPP.
Min Z 4x1 x2
Subject to
0
3 6
3 2 4
2 5
1 2
1 2
1 2
1 2




x x
x x
x x
x x
12. Solve by graphical method, the following LPP
Max Z 4x1 3x2 Subject to
0
700
400
800
2 1000
1 2
2
1
1 2
1 2





x x
x
x
x x
x x
Or
Solve the following assignment problem for
minimization
a b c d e
A 85 75 65 125 75
B 90 78 66 132 78
C 75 66 57 114 69
D 80 72 60 120 72
E 76 64 56 112 68
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13. Describe the characteristics of queueing system.
Or
Explain the calculations performed in single server
queueing models.
14. Define the various time estimates in a network.
Or
What are the calculations performed in a CPM
network.
15. Explain the problem of sequencing and its use.
Or
Define the basic terms used in sequencing.
Part C 10 30)
Answer any three questions.
16. Solve the following LPP using simplex method
Max Z 4x1
Subject to
0.
2 3 90
2 5 100
2 50
1 2
1 2
1 2
1 2




x x
x x
x x
x x
17. Solve the following transportation problem for
minimization.
D1 D2 D3 D4 Available
A1 6 1 9 3 70
A2 11 5 2 8 55
A3 10 12 4 7 90
Demand 85 35 50 45
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18. In a railway marshalling yard, goods trains arrive at a
rate of 30 trains per day. Assuming that the inter-arrival
time follows an exponential distribution and the service
time distribution is also exponential with an average 36
minutes. Calculate the following.
the mean queue size and
the probability that the queue size exceeds 10.
19. The following information is provided regarding a
project
Activity 1-2 2-3 2-4 3-5 4-6 5-6 5-7 6-7
Optimistic 3 3 2 4 4 0 3 2
Pessimistic 3 9 6 8 8 0 5 8
Most likely 3 6 4 6 6 0 4 5
Draw the project network
Calculate the expected duration and variance of
each activity.
Find the critical path and the expected project
length.
20. A book binder has one printing press, one binding
machine, and the manuscripts of a number of different
books. the time required to perform the printing and
binding operations for each book is shown below.
Determine the order in which books should be processed,
in order to minimize the total time required to turn out
all the books
Book 1 2 3 4 5 6
Printing time 30 120 50 20 90 100
Binding time 80 100 90 60 30 10