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Cms 300: Operation Research Ii Question Paper
Cms 300: Operation Research Ii
Course:Bachelor Of Commerce
Institution: Kca University question papers
Exam Year:2009
1
UNIVERSITY EXAMINATIONS: 2008/2009
THIRD YEAR STAGE 1 EXAMINATION FOR THE DEGREE OF
BACHELOR OF COMMERCE
CMS 300: OPERATION RESEARCH II
DATE: APRIL 2009 TIME: 2 HOURS
INSTRUCTIONS: Answer question ONE and any other TWO questions
QUESTION ONE (30 MARKS).
(a) explain the following terms;
(i) Network
(ii) Shortest route problem
(iii) Minimum span problem
(iv) Group replacement policy
(v) Transition matrix
(10 Marks)
(b) A market survey is made on three brands of breakfast foods X, Y and Z. Every time the
customer purchases a new package, he may buy the same or switch to another brand. The
following estimates are obtained, expressed in decimal fractions:
? ? ?
?
?
? ? ?
?
?
0.3 0.3 0.4
0.3 0.5 0.2
0.7 0.2 0.1
Z
Y
X
X Y Y
At this time it is estimated that 30 per cent of the people buy brand X, 20 per cent brand Y and 50%
per cent Z. What will the distribution of customers be in
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(i) Two time periods late (5 Marks)
(ii) At equilibrium (7 Marks)
(c) Explain the following types of replacements policies
(i) Individual replacement policy (3 Marks)
(ii) Group replacement policy (3 Marks)
(d) Explain the benefits of LINGO programming language (2 Marks)
QUESTION TWO
(a) Giving examples, explain any two categories of mathematical models. (4 Marks)
(b) Explain two Categories of replacement of items (4 Marks)
(c) The following failure rates have been observed for a certain type of light bulb:
End of week 1 2 3 4 5 6 7 8
Probability of failure to
date
0.05 0.13 0.25 0.43 0.68 0.88 0.96 1.00
Given that the number of light bulbs in the beginning are 100, and the cost of replacing an individual
failed bulb is Kshs 35. The decision is made to replace all bulbs simultaneously at fixed intervals, and
also to replace individual bulbs as they fail in services. If the cost of group replacement is Kshs 30 per
bulb;
(i) Find the best interval between group replacements. (8 Marks)
(ii) Find at what group replacement price per bulb would a policy of strictly individual
replacement become preferable to the adopted policy. (4 Marks)
QUESTION THREE
(a) Define the term Shortest route problem (2 Marks)
(b) Explain Five steps involved in solving the shortest route problem (5Marks)
(c) An individual who lives in Thika, Kenya and works in Westlands in Nairobi seeks a car route
that will minimize the morning driving time (in minutes). This person has recorded driving
time along major high ways between different intermediate points/towns. This data is shown in
the table below
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Thika Juja Kasaran
i
Kiambu Forest
road
Westlands
Thika 8 32
Juja 8 15 28
Kasarani 15 13 32
Kiambu 32 28 13 10 13
Forest road 10 5
Westlands 32 13 5
A blank entry symbolizes that no major highway links between the corresponding points.
(i) Develop a master list for the above problem. (3 Marks)
(ii) Determine the minimum time this individual takes to travel from Thika to Westlands
(6 Marks)
(iii) Determine the best commuting route for this individual. (2 Marks)
(d) Give any two rules in declaring variables in a LINGO programming language (2 Marks)
QUESTION FOUR
(a) Explain the following terms as used in markov chains
(i) An ergodic state (2 Marks)
(ii) Steady state (2 marks)
(b) Explain any two areas of application of Markov analysis (4 marks)
(c) On January 1st (this year), bakery A had 40% of its local market share while the other bakeries
B and C had 40% and 20%, respectively of the market share. Based upon a study by a
marketing research firm, the following facts were compiled. Bakery A retains 90% of its
customers while gaining 5% of competitor B’s customers and 10% of C’s customers. Bakery B
retains 85% of its customers while gaining 5% of A’s customers and 7% of C’s customers.
Bakery C retains 83% of its customers and gains 55% of A’s customers and 10% of B’s
customers.
(i) Find the market share for each firm on January 1st, next year (4 Marks)
(ii) Find the market share for each firm in the long run (8 Marks)
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QUESTION FIVE
(a) A fleet owner finds from his past records that the costs per year of running a truck whose
purchase price is US$ 6,000 are given below:
Year: 1 2 3 4 5 6 7
Running cost (US$): 1000 1200 1400 1800 2300 2800 3400
Resale value (US$): 3000 1500 750 375 200 200 200
Determine when the equipment should be replaced (7Marks)
(b) Define a general non linear programming problem (5 Marks)
(c) A Manufacturing concern produces a product consisting of two raw materials, A1, and A2. The
production function is estimated as
2
2 2
2
1 2 1 1 z = f (x , x ) = 3.6x - 0.4x +1.6x - 0.2x
where z represents the quantity (in tons) of the product produced, and 1 x and 2 x designate the
input amounts of raw materials A1 and A2. The company has US$ 50,000 to spend on these
two raw materials. The unit price of A1 is US$ 10,000 and A2 is US$ 50,000. Determine how
much input amounts of A1 and A2 be decided so as to maximize the production output.
(8 Marks)
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