LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034
B.A. DEGREE EXAMINATION – ECONOMICS

THIRD SEMESTER – APRIL 2006
ST 3100 – RESOURCE MANAGEMENT TECHNIQUES
(Also equivalent to STA 100)
Date & Time : 02052006/1.004.00 P.M. Dept. No. Max. : 100 Marks
PART – A
Answer all the questions. 10 ´ 2 = 20
 Define slack and surplus variables in an LPP.
 State any two applications of linear programming problem.
 What is a transportation problem?
 How to balance an unbalanced transportation problem?
 What is the need for an assignment problem?
 Define critical activity.
 Explain i). Most likely time ii). Optimistic time in network analysis.
 What is the objective of sequencing problem?
 Define i). Holding cost, ii). Shortage cost.
 What is an economic order quantity (EOQ) in inventory control?
PART – B
Answer any five questions. 5 ´ 8 = 40
 A Company has 3 operational departments (weaving, processing and packing) with capacity to produce 3 different types of clothes namely suiting, shirting’s and woolens yielding a profit of Rs. 2, Rs. 4 and Rs. 3 per meter respectively. One meter of suiting requires 3 minutes in weaving, 2 minutes in processing and 1 minute in packing, similarly one meter of shirting requires 4 minutes in weaving, 1 minute in processing and 3 minutes in packing, one meter of woolen requires 3 minutes in each department. In a week, total time of each department is 60, 40 and 80 hours for weaving processing and packing respectively.
Formulate the linear programming problem to find the product mix to maximize the profit.
 Solve graphically.
Max Z = 5x_{1} + 3x_{2}
Subject to: x_{1} + 2x_{2} £ 18
x_{1} + x_{2} £ 9
0 £ x_{2} £ 6
0 £ x_{1} £ 4
 Find the starting solution in the following transportation problem by least lost method.
Origin  D1  D2  D3  Supply 
O1  16  20  12  200 
O2  14  8  18  160 
O3  26  24  16  90 
Demand  180  120  150 
 A department head has 4 subordinate and 4 jobs to be performed. The time taken by each man to complete the job is given below.
Job 
Men 

A  1  2  3  4  
B  18  26  17  11  
C  13  28  14  26  
D  38  19  18  15  
E  19  26  24  10 
How should the jobs be assigned to minimize the time?
 In a factory there are six jobs to perform, each of which should go through two machines A and B in the order A, B. the processing timings (hrs) for the jobs are given below.
Job  1  2  3  4  5  6 
Machine A  1  3  8  5  6  3 
Machine B  5  6  3  2  2  10 
Find the sequence that would minimize the total elapsed time.
 A small project consists of 7 activities for which the relevant data are given below.
Activity  Preceding Activities  Duration 
A  ———  4 
B  ———  7 
C  ———  6 
D  A, B  5 
E  A, B  7 
F  C, D, E  6 
G  C, D, E  5 
Draw the arrow diagram and find the critical path.
 Explain in detail ABC analysis in inventory control.
 Explain how will you obtain the economic order quantity for a single item static model in inventory control.
PART – C
Answer any two questions. 2 ´ 20 = 40
 Solve the following linear programming problem by simplex method. Maximize Z = 4x_{1} + 10x_{2}
Subject to 2x_{1} + x_{2} £ 50
2x_{1} + 5x_{2} £ 100
2x_{1} + 3x_{2} £ 90
x_{1}, x_{2} ³ 0.
 A manufacturer has distribution centers X, Y and Z. his retail outlets are A, B, C, D and E. the transport cost per unit between each center outlet is given below:
Retail outlet  
Distribution Center 
A  B  C  D  E  Supply  
X  55  30  40  50  50  40  
Y  35  30  100  45  60  20  
Z  40  60  95  35  30  40  
Demand  25  10  20  30  15 
Find the optimum solution to the given transportation problem.
 A project consists of eight activities with the following relevant information.
Activity  Immediate predecessor  Optimistic time  Most likely time  Pessimistic
time 
A  ——  1  1  7 
B  ——  1  4  7 
C  ——  2  2  8 
D  A  1  1  1 
E  B  2  5  14 
F  C  2  5  8 
G  D, E  3  6  15 
H  F, G  1  2  3 
 Draw the PERT network
 Find the expected completion time and variance of each activity.
 Find the total float and free float.
 What is the probability of completing the project in time?
 a). Explain the various problems involved in the inventory management.
b). Explain in detail a single item static model with one price break with the necessary diagrams
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