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University of Madras (UoM)

University of Madras (UoM)

Syllabus

Test Papers

Permission for writing BE/BTech/BArch/ME Exams

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Quantitative Techniques
Quantitative Techniques
October 2003
U/IC 5207/PXD

Time: Three hours
Maximum: 100 marks

SECTION A - (5 x 8 = 40 marks)

Answer any FIVE questions.
All questions carry equal marks.

1. a. State any two types of models used in OR

b. Define LP Problem.

c. Can a Transportation problem be regarded as a special case of LP problem? Justify your answer.

d. Find the initial b.f.s for the following transportation problem by North – West corner method:

Destination
Sources   D1 D2 D3 Supply
O1 2 3 11 9
O2 1 9 6 6
Demand 7 5 3  

e. State Baye’s Theorem

f. Define saddle point.

g. State any 2 components of a network

h. Draw the network for the activities described below:
Activity A B C D E F G H
Immediate Predecessor - - A B C,D C,D E F


i. Describe the queuing model: (M/M/C): (&infinity;/LIFO).

j. Explain the concept : Service discipline

SECTION B - (5 x 6 = 30 marks)

Answer any FIVE questions.
All questions carry equal marks.

2. What are the advantages or OR in decision making?

3. Explain the terms: feasible solution, degenerated basic feasible solution, unbounded solution

4. Find the saddle point, if exists:

Player B
Player A   1 2 3 4
1 0 7 5 12
2 10 11 9 13
3 9 5 7 2


5. What are the assumptions made in solving a project scheduling by CPM/PERT?

6. Explain the least-cost method to find an initial b.f.s of a transportation problem.

7. Explain Kendall’s notation for queuing models.

8. A fertilizer company distributes its products by trucks. It was found that on an average every 5 minutes one truck arrived and the average loading time was 3 minutes. Determine:

a. the probability that a truck has to wait.
b. average waiting time of a truck.

SECTION-C (2x20=40 marks)

Answer BOTH the questions.
All questions carry equal marks.

9. a. Solve the following LP problem by graphical method:
Maximize z = 28x + 30y
Subject to:
6x + 3y ≤ 18
3x + y ≤ 8
4x + 5y ≤ 30
and x,y ≥ 0

b. Solve the following transportation problem:

Destination
Problem   1 2 3 4  
A 11 22 6 5 75
B 16 31 14 15 60
C 5 21 4 9 40
    30 65 55 25  


10. a. Draw the network for the following project:

Activity A B C D E F G
Immediate Predecessor - - - A B C D,E
Duration (Days) 2 4 3 1 6 5 7
Compute the critical path and float for each activity.

Or

b. Write short notes on:

i. Decision trees

ii. Time estimates used in PERT

iii. Poisson queues

iv. Balanced and unbalanced transportation
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