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Cms 300 Operations Research Ii Question Paper
Cms 300 Operations Research Ii
Course:Bachelor Of Commerce
Institution: Kca University question papers
Exam Year:2011
UNIVERSITY EXAMINATIONS: 2011/2012
YEAR III EXAMINATION FOR THE BACHELOR OF COMMERCE
CMS 300 OPERATIONS RESEARCH II
(EVENING)
DATE: APRIL 2012 TIME: 2 HOURS
INSTRUCTIONS: Answer Question One and Any other Two Questions
QUESTION ONE
a) State and critic the assumptions of markov chains (5 Marks)
b) Write short notes on replacement policies of
i. Capital items (5 Marks)
ii. Items that fail suddenly (5 Marks)
c) Kagoro Village consists of a total of 1600 household. A market research firm gathered data in
an attempt to investigate the loyalty of these households for a particular brand of toilet soap X,
Y and Z sold in the village shops. A customer survey at the end of Dec. 2010 revealed the
following brands switching patterns.
T O
X Y Z
FROM X
Y
Z
400
100
60
50
350
180
50
50
360
Required:
a) Determine the transition matrix for the above Markov process.
b) Determine the steady state distribution of the usage of the three types of toilet soap. (15 Marks)
2
QUESTION TWO
A certain type of fluorescent tube has the following failure rates
End of month
Cumulative
Probability failure
1 0.03
2 0.12
3 0.25
4 0.40
5 0.68
6 0.88
7 0.98
8 1.00
The firm uses 4,000 tubes in its premises. The cost of replacing an individual tube is shs.50. A
decision is made by the management of the firm to replace all tubes either simultaneously at fixed
intervals or to replace individual tubes as and when they fail. If the cost of group replacement is shs.25
per tube.
Required:
a) Assuming group replacement is done at end month, what is the best interval between group
replacement?
b) At what group replacement price per tube should a policy of strictly individual replacement
become preferable to the adopted policy in a above? (20 Marks)
QUESTION THREE
a) Define the following terms as used in Markovian analysis:
(i) Transition matrix (2 Marks)
(ii) Initial probability vector (1 Mark)
(iii) Equilibrium (1 Mark)
(iv) Absorbing state (2 Marks)
b) Boots Ltd. Manufactures a range of five similar products, A, B, C, D and E. The table below
shows the quantity of each of the required inputs necessary to produce one unit of each product,
together with the weekly inputs available and selling prices of each product.
3
Inputs
A
B C D E Weekly inputs
available
Raw material (kg)
Forming (hours)
Firing (hours)
Packing (hours)
Selling price (sh.)
6.0
1.00
3.00
0.50
40
6.5
0.75
4.50
0.50
42
6.1
1.25
6.00
0.50
44
6.1
1.00
6.00
0.75
48
6.4
1.00
4.50
1.00
52
35,000 kgs
6,000 hours
30,000 hours
4,000 hours
The cost of each input is as follows:
Material Sh.2.10 per kg
Forming Sh.3.00 per hour
Firing Sh.1.30 per hour
Packing Sh.8.00 per hour
Required:
A Lindo and Lingo programs for the above problem assuming it is a general integer problem
(14 Marks)
QUESTION FOUR
The following information was by power utility firm that wanted to connect electricity from point A to
G. The distance between AB and BC is 2km,between AC and EG is 5km,between AD,CE and DF is
4km,between CD and EF is 1km,between CF is 3km, between BE and FG is 7km.
Required:
a) Draw a network diagram (5 Marks)
b) Determine the minimum distance interconnecting the points. (5 Marks)
c) Solve the following optimization problem using Lagrangian multiplier approach
Min Z= X1^2+X2^2+X3^2
Subject to
X1+X2+X3=2
5X1+2X2+X3=5
X1,X2,X3 >=0
4
(10 Marks)
Question Five
A motorist is located in city 1 decided to travel to a city 8. He knew the distances in km of alternative
routes from 1 to 8. He then drew a highway network map as shown in the diagram below.
1 2 3 4 5 6 7 8
1 1040 1060 1030
2 2070 3000 2050
3 2030 2080 2040
4 1060 1080 1050
5 1040
6 2030
7 2080
8
The magnitude of the distance between cities 1-2 is the same as 2-1 etc and that the blank spaces
indicate that the routes are infeasible eg 1-1, 1-5, 3-8, etc.
Required:
a) Draw a network diagram to represent the movement from origin (city 1) to destination or
sink (city 8) clearly indicating the stages and nodes (10 Marks)
b) Using dynamic programming algorithm, determine the path and hence the shortest route in km
for the problem (10 Marks)
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