B.Sc. DEGREE EXAMINATION
– STATISTICS
SIXTH SEMESTER
– APRIL 2006
AC 23
ST 6601 - OPERATIONS RESEARCH
(Also equivalent to STA 601)
Date & Time : 21-04-2006 /9.00-12.00
Dept. No. Max. : 100 Marks
SECTION A (10 x 2 =20)
Answer ALL the questions. Each carries two Marks
1.
Define saddle point of a pay-off matrix
2.
How many basic cells will be there in a starting solution where there are 4 destinations and 3 origins in a transportation problem ?
3.
Distinguish between “pure” and “mixed” strategies
4.
What is a minimal spanning tree ?
5.
How do you identify the critical activities of a project ?
6.
Give the formula for free float and total float corresponding to an activity defined by arcs i and j
7.
How will you conclude the presence of more than one optima for an LPP ?
8.
What is an unbalanced transportation problem ?
9.
Give the fundamental difference between PERT and CPM
10.
In what way Floyd’s algorithm is superior to Dijkstra’s algorithm ?
SECTION B (5 x 8 =40)
Answer any FIVE of the following. Each carries EIGHT marks
11.
Diamond is an aspiring young student of Loyola College. He realizes that “all work and no play makes him a dull boy”. As a result, Diamond wants to apportion his available time of about 10 hours a day between work and play. He estimates that play is twice as much fun as work. He also wants to study at least as much as he plays. However, Diamond realizes that if he is going to get all his homework assignments done, he can not play more than 4 hours a day. How should Diamond allocate his time to maximize his pleasure from both work and play ?
12.
Comment on the solution of the following LPP
Maximize
Subject to z x

2 x
1 x
1
1
,
2 x
1
 x
2
 x
2


40

0 x
2
10
13.
Specify the range for value of the game in the following case assuming that the payoff is for player A
B1 B2 B3 B4
A1 1
A2
A3
A4
2
-5
7
9
3
-2
4
6
8
10
-2
0
4
-3
-5

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14.
Use the Hungarian method to solve the following Assignment Problem
$3 $9 $2 $3 $7
$6 $1 $5 $6 $6
$9 $4 $7 $10 $3
$2 $5 $4 $2 $1
$9 $6 $2 $4 $5
15.
Write the following problem in standard form :
Maximize z
Subject to

2 x
1

3 x
2

5 x
3
 x
1
6 x
1

 x
2 x
1
, x
3

7 x
2

4
 x
3
0
9
 x
3
10

4 x
2
unrestricted and also form the initial simplex table (No need to solve the problem)
16.
Obtain the minimal spanning tree corresponding to the following network
3
2
1
6
5
9
5
3
10
7 5 8
4 3
6
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17.
Draw the time schedule for the following network and identify red flagged activities
11
0
0
1
2
5
B
3
4
13
13
0
5
F
1
18.
Express a transportation problem as Linear programming problem.
SECTION C (2x 20=40)
6
Answer any TWO of the following. Each carries TWENTY marks.
19.
Solve the following problem using big-M method
Maximize z
 x
1

5 x
2

3 x
3 subject to x
1

2 x
2
 x
3

3
2 x
1 x
,
1 x
 x
2
2
, x
3


4
0
20.
Solve the following network problem using Floyd’s algorithm
2
5
3 4
1
10
3
6
15
4
5
2
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21.
Solve the following 2 x 4 game graphically
B1 B2 B3 B4
A1 2 2 3 -1
A2 4 3 2 6
22.
Find the critical path corresponding to the following project network and draw the time schedule
1
`
I 1
A 5
C 8
5
2
B 10
D 9
F 10
E 4
J 7
3
G 3
6
H 5
K 3
L 8
M 4
7
4
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