# LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034 ```LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034
B.A. DEGREE EXAMINATION – ECONOMICS
SUPPLEMENTARY EXAMINATION – JUNE 2007
ST 3100 - RESOURCE MANAGEMENT TECHNIQUES
Date &amp; Time: 26/06/2007 / 9:00 - 12:00
Dept. No.
Max. : 100 Marks
PART-A
10x2=20 marks
01. Define a general linear programming problem.
02. Define slack and surplus variables.
03. Express a transportation problem as a linear programming problem.
04. Assignment problem is a particular case of transportation problem-Justify.
05. Distinguish between CPM and PERT.
06. When is an activity called critical in a network?
07. Define a non-degenerate solution to a transportation problem.
08. What is the need for inventory?
09. Define (i) time horizon (ii) lead time.
10. Write a note on (a) holding cost (b) penalty cost.
PART-B
11. Solve graphically the following L.P.P.:
Maximize Z=3x1+2x2
Subject to the constraints:
-2x1+x2  1
x1
2
x1+x2  3
x1,x2  0
5x8=40 marks
12. Obtain all the basic solutions to the following system of linear equations:
x1 +2x2+x3 = 4
2x1 +x2+5x3 = 5
13. Find the initial solution using VAM for the following transportation problem:
Destination
Origin
Availability
D1
D2
D3
D4
O1
1
2
1
4
30
O2
3
3
2
1
50
O3
4
2
5
9
20
Requirement
20
40
30
10
14. Solve the following assignment problem:
A
B
C
D
I
1
4
6
3
II
9
7
10
9
III
4
5
11
7
IV
8
7
8
5
15. In a factory ,there are six jobs to perform ,each of which should go through two machines A and
B ,in the order A and B.The processing timings(in hours) for the jobs
are given here.Determine the sequence for performing the jobs that would minimize
the total elapsed time T.What is the value of T?
Job:
J1
J2
J3
J4
J5
J6
Machine A : 1
3
8
5
6
3
MachineB : 5
6
3
2
2
10
16. The following table gives the activities of a construction project and duration.
Activity:
1-2
1-3 2-3
2-4 3-4
4-5
Duration(Days) : 20
25
10
12
6
10
(i)
Draw the network for the project.
(ii)
Find the critical path.
17. Explain ABC analysis in inventory control.
18. Derive a single item static model clearly stating the assumptions.
PART-C
2x20=40marks
19. Use big M method to
Minimize Z=4x1+3x2
subject to the constraints:
2x1+x2  10
-3x1+2x2  6
x1 + x2
6
x1, x2  0
20. Find the optimum solution to the following transportation problem:
Warehouse
Factory
capacity
D
E
F
G
A
42
48
38
37
160
B
40
49
52
51
150
C
39
38
40
43
190
Demand
80
90
110
160
2
21. The following table lists the jobs of a network along with their time estimates:
Job
Duration(days)
i
j
optimistic most likely pessimistic
1
1
2
2
3
4
6
5
7
2
6
3
4
5
5
7
8
8
3
2
6
2
5
3
3
1
4
6
5
12
5
11
6
9
4
19
15
14
30
8
17
15
27
7
28
(a) Draw the project network.
(b) Calculate the length and variance of the critical path.
(c) What is the probability that the project will be completed in 41 days?
22. Explain a single item static model with one price break with the necessary diagrams.
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