B.A. DEGREE EXAMINATION
– ECONOMICS
SUPPLEMENTARY EXAMINATION
– JUNE 2009
ST 3103 - RESOURCE MANAGEMENT TECHNIQUES
Date & Time: 26/06/2009 / 10:00 - 1:00 Dept. No. Max. : 100 Marks
PART-A
Answer ALL the following:
1) Define Linear Programming.
2) Define feasible solution.
3) Briefly explain transportation problem.
4) When do we say an assignment problem is called an unbalanced?
5) Define Network Scheduling.
6) What is meant by the total elapsed time in sequencing problem?
7) Write down any two differences between CPM and PERT.
8) Define holding and penalty cost?
9) What is Lead time?
10) What is Economic Order Quantity?
(10X2=20)
PART-B
Answer any FIVE of the following: (5X8=40)
11) Old hens can be bought for Rs.2 each but young ones cost Rs.5 each. The old hens lay 3 eggs per week and the young ones 5 eggs per week, each being worth
30 paise. A hen costs Re.1 per week to feed. If I have only Rs.80 to spend for hens, how many of each kind should i buy to give a profit of more than Rs.6 per week, assuming that i cannot house more than 20 hens? Write a mathematical model of the problem.
12) Solve the given problem using graphical method:
Maximize z = 1.75x
1
+ 1.5x
2
subject to the constraints: 8x
1
+ 5x
2

320
4x
1
+5x
2

200
x
1

15, x
2
x
1, x
2

0 .

10
13) Use simplex method to solve the following L.P.P:
Maximize Z = x
1
– x
2
+ 3x
3
subject to the constraints: x
1
+ x
2
+ x
3

10
2x
1
– x
3

2
2x
1
- 2x
2
+3x
3

0
x
1, x
2, x
3

0 .
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14) Four professors are each capable of teaching any one of four different courses.
Class preparation time in hours for different topics varies from professor to professor and is given in the table below. each professor is assigned only one course so as to minimize the total course preparation time for all courses:
Professor
A
B
C
D
Linear programme
2
15
13
4
Queueing
Theory
10
4
14
15
Dynamic
Programme
9
14
16
13
Regression
Analysis
7
8
11
9
15) Find the I.B.F.S for the following problem using (i) North-west corner rule
(ii) Least cost method.
Destination
Origin
O
1
O
2
O
3
D
1
3
4
1
D
2
3
2
2
D
1
2
5
3
D
4
1
9
4
Availability
30
50
20
Requirement 20 40 30 10
16) Six jobs go first over machine I and then over machine II. The order of the completion of jobs has no significance. The following table gives the machine times in hours for six jobs and the two machines:
Job no. 1
Time on Machine I 5
Time on machine II 7
2
9
4
3
4
8
4
7
3
5
8
9
6
6
5
Find the sequence of jobs that minimizes the total elapsed time to complete the jobs.
17) Draw the network diagram and find the critical path for the following:
Activity A B C D E F G H I J k
Time taken 2 2 1 4 5
The constraints for the job are as follows:
8 3 1 4 5
A < D; B < E,F; C < G; D < H; E < I; H,I < K; F,G < J.
18) Neon lights on the campus are replaced at the rate of 100 units per day. The physical plant orders the neon lights periodically. It costs $100 to initiate a purchase order. A neon light kept in storage is estimated to cost about $ 0.02 per day. The lead time between placing and receiving an order is 12 days. Determine the optimal inventory policy for ordering the neon lights.
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PART-C
Answer any TWO of the following:
19) Solve the following L.P.P using Penalty method:
(2X20=40)
Maximize Z = 40,000x
1
+ 55,000x
2
Subject to the constraints: 1000x
1
+ 1500x
2

20,000
x
1

12 , x
x
1
, x
2

0.
2

5
20) There are three sources or origins which store a given product. These sources
supply these products to four dealers. The capacities of the sources and the
S
1
S
2
demands of the dealers are given below:
Demand
Source D
1
27
10
D
2
23
45
D
3
31
40
D
4
69
32
Capacity
150
40
S
3
30
Requirement 90
54
70
35
50
57
60
80
Find out the optimal solution for transporting the products at a minimum cost
using VAM .
21) A small assembly plant assembles PCs through 9 interlinked stages according to following process:
Activity 1-2 1-3 1-4 2-5 2-6 3-6 4-7 5-7 6-7 t o
5 18 26 16 15 6 7 7 3 t p t m
10
8
22
20
40
33
20
18
25
20
12
9
12
10
9
8
5
4
Determine the following:
(i) expected task time and their variance.
(ii) The earliest and latest expected times to reach each node.
(iii) The critical path and
(iv) The probability of a node occurring at the proposed completion date if the original contract time of completing the project is 41.5 weeks.
22) Derive EOQ models with Price breaks. (20)
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