LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034
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B.Sc. DEGREE EXAMINATION – STATISTICS
THIRD SEMESTER – APRIL 2008
ST 3103 / 3100 – RESOURCE MANAGEMENT TECHNIQUES
Date : 07/05/2008 Dept. No. Max. : 100 Marks
Time : 9:00 – 12:00
SECTION- A
Answer all the questions. 10×2 = 20 marks
1.Define operations research.
2.Explain the need for slack and surplus variables in an LPP.
3.Define basic solution for an LPP.
4.State the objective of a transportation problem.
5.Express an assignment problem as an LPP.
6.Distinquish between CPM and PERT.
7.When is an activity in a network analysis called critical ?
8.Define degenerate solution for a transportation problem.
9.What is time horizon and lead time in inventory ?
10 Write a short note on setup and shortage costs.
SECTION –B
Answer any five questions. 5×8 = 40 marks
11.Obtain all the basic solutions to the following system of linear equations:
2x1 + x2 – x3 = 2
3x1 + 2x2 + x3 = 3.
12.Solve graphically the following LPP:
Max Z = 7x1 + 3x2
Subject to the constraints:
x1 + 2x2 3
x1 + x2 4
x1 5/2
x2 3/2
x10 & x2 0.
13.Find an initial solution for the following transportation problem using least cost
method:
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.Six wagons are available at six stations A,B,C,D,E and F. These are required at
stations I,II,III,IV,V and VI. The following table gives the distances(in kilometers)
between various stations:
I II III IV V VI
A 20 23 18 10 16 20
B 50 20 17 16 15 11
C 60 30 40 55 8 7
D 6 7 10 20 100 9
E 18 19 28 17 60 70
F 9 10 20 30 40 55
How should the wagons be assigned so that the total distance covered is minimized ?
- A small maintenance project consists of the following 12 jobs:
Job Duration(in days)
- 2
2-3 7
2-4 3
3-4 3
3-5 5
4-6 3
5-8 5
6-7 8
6-10 4
7-9 4
8-9 1
9-10 1
(a) Draw the arrow diagram of the project.
(b) Determine the critical path and the project duration.
- Use simplex method to solve the following LPP:
Max Z = 3x1 + 2x2
Subject to the constraints:
x1+ x2 4
x1 – x2 2
x10, x20
- Explain the inventory control of a system.
- Derive a single item static model with the necessary diagram.
SECTION-C
Answer any two questions. 2×20 = 40 marks
- Use big M method to
Min Z = 4x1+ 3x2
Subject to the constraints:
2x1 + x2 10
-3x1 +2x2 6
x1 + x2 6
x10,x20
- Consider the following transportation table showing production and transportation
costs , along with the supply and demand positions of factories/distribution centres:
M1 M2 M3 M4 Supply
——————————————————————————-
F1 4 6 8 13 500
F2 13 11 10 8 700
F3 14 4 10 13 300
F4 9 11 13 3 500
——————————————————————————–
Demand 250 350 1050 200
(a) Obtain an initial basic feasible solution by using VAM.
(b) Find the optimal solution for the above given problem.
- A project is composed of eleven activities ,the time estimates for which are given below:
——————————————————————————————————-
Activity optimistic time normal time pessimistic time
(days) (days) (days)
——————————————————————————————————–
1-2 7 9 17
1-3 10 20 60
1-4 5 10 15
2-5 50 65 110
2-6 30 40 50
3-6 50 55 90
3-7 1 5 9
4-7 40 48 68
5-8 5 10 15
6-8 20 27 52
7-8 30 40 50
(a) Draw the network diagram for the project.
(b) Find mean and variance of the activities.
(c) Determine the critical path.
(d) What is the probability of completing the project in 125 days ?
22.(a) Derive the single item static model with one price break with the necessary diagrams.
(b) LubeCar specializes in fast automobile oil change.The garage buys car oil in bulk
at $3 per gallon.A price discount of $2.50 per gallon is available if LubeCar
purchases more than 1000 gallons.The garage services approximately 150 cars per
day,and each oil change requires 1.25 gallons. LubeCar stores bulk oil at the cost
of $0.02 per gallon per day.Also the cost of placing an order for bulk oil is
$20.There is a 2 day lead time for delivery.Determine the optimal inventory policy.
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