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Cms 300 Operations Research Ii-Sunday Question Paper
Cms 300 Operations Research Ii-Sunday
Course:Bachelor Of Commerce
Institution: Kca University question papers
Exam Year:2011
1
UNIVERSITY EXAMINATIONS: 2010/2011
EXAMINATION FOR THE BACHELOR OF COMMERCE
CMS 300 OPERATIONS RESEARCH II-SUNDAY
DATE: DECEMBER 2011 TIME: 2 HOURS
INSTRUCTIONS: Answer Question ONE and any other two Questions
QUESTION ONE
a) State the characteristics of Markov chains (5 marks)
b) Differentiate between a recurrent state and transient state (4 marks)
c) (i) A firm is considering six possible products to launch. Information on the same is as
follows
product Initial
capital(sh000)
salesmen required profits(sh000)
d1 1050 3 500
d2 1700 5 950
d3 750 2 400
d4 300 1 150
d5 2700 8 1100
d6 1750 3 750
Maximum
available
5000
12
2
Formulate (but do not solve) a LINDO or LINGO integer programming model for the
problem assuming binary variables (7 marks)
(ii) An extract of the final solution tableau (sh000) for the problem above was
Variable Value Reduced cost
d1 1 -500
d2 1 -950
d3 0 -400
d4 1 -150
d5 0 -1100
d6 1 -750
Row Slack or surplus Dual price
2) 200 0
3) 0 0
Where Pi(i=1,2…6) represent product i.
Determine which products are chosen and the maximum profits.
Explain the meaning of sh 200, 000 in the slack/surplus column. (14 marks)
Total 20 marks
QUESTION TWO
The driver of a certain route in town has various options moving a load from center A to G. The
following represents the allowable tonnage from a center to the other. The loads can be moved in
either direction but not necessarily the same amount eg from A to B is 200 kg but from B to A is
400kg. No load is permissible in the blank spaces.
To/from
3
From/to
Required:
a) A network diagram for the flow from A to G (10 marks)
b) The maximal flow path and load in kilogram’s (10 marks)
Total 20 marks
QUESTION THREE
a) A truck costs £300,000. The annual running cost and the resale price in a given year is as
follows:-
Year (End) 1 2 3 4 5 6 7
Running cost £ 60,000 70,000 80,000 90,000 100,000 120,000 150,000
Selling price £ 200,000 133,333 100,000 75,000 50,000 30,000 30,000
If such type of truck will be used for the foreseeable future, how frequently should it be
replaced? What assumptions have you made? (5 marks)
b) The truck in (a) above may be replaced by a second hand one, which may be one, two up to six
years old. The cost of buying a truck of various ages follows:
Age of truck (years) 1 2 3 4 5 6
Purchase price (£ 000) 230 160 130 100 70 50
Required; Given this possibility, determine the optimal age to buy and sell the truck. (10 marks)
c) Evaluate the following using the Lagrange multiplier approach
Max Z= x2+2x+4y+y2
s.t 5x+2y= 24
4x+6y=40
x,y= 0
(5 marks)
Total 20 marks
A B C D E F G
A 200 800 1100 900
B 400 300 500 100
C 100 400 200
D 500 900 200 2300
E 200 800 700 900
F 800 300 500 100 1000
G 1000 400 200
4
QUESTION FOUR
A salesman located in city 1 decided to travel to a city 10. He knew the distances in KMS of
alternative routes from A to B. He then drew a highway network map as shown in the diagram
below.
1 2 3 4 5 6 7 8 9 10
1 14 16 13
2 27 30 25
3 23 28 24
4 16 18 15
5 14 18
6 23 27
7 28 24
8 37
9 39
10
The magnitude of the distance between cities 1-6 is the same as 6-1 etc and that the blank
spaces indicate that the routes are infeasible eg 1-1, 1-5, 3-8, etc.
Required: Using dynamic programming algorithm,
a) Draw a network diagram to represent the movement from origin (node1) to destination or
sink(node 10) clearly indicating the stages and nodes (10 marks)
b) Determine the path and hence the shortest route in KMS for the problem (10 marks)
Total 20 marks
QUESTION FIVE
You are a Senior Audit Assistant of Abel Adongo & Co., Certified Public Accountant. The firm is
one of the three accounting firms offering professional services in the city of Modavia. The other
two firms are Bean Birindu & Co., Certified Public Accountants and Claudio Chege & Co
Certified Public Accountants. The three firms are referred to as A, B and C. Your firm is worried
about its market share and the Senior Partner in charge of Partnership development has collected
the following data which she wants you to analyse. She further informs you that the observed
client flow behaviour is expected to remain about the same for the foreseeable future.
No. of
Market
Flow of Clients
No. of
Gains From Losses To Market
5
clients share Clients share
31.12.90 A B C A B C 31.12.91
A 204 0.177 - 12 20 - 15 9 212 0.184
B 416 0.361 15 - 5 12 - 7 417 0.362
C 531 0.462 9 7 - 20 5 - 522 0.454
Required
a) Convert the above data into a matrix of transition probabilities. (5 marks)
b) Estimate the firm’s market shares for 1992. (5 marks)
c) Estimate the firm’s steady state market shares. (7 marks)
d) Briefly comment on the advisability of using the Markov Technique in forecasting market
shares in the market for accountancy services. (3 marks)
(Total: 20 marks)
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