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Operations Research Ii Question Paper

Operations Research Ii

Course:Bachelor Of Commerce

Institution: Kca University question papers

Exam Year:2010

UNIVERSITY EXAMINATIONS: 2010/2011
THIRD YEAR EXAMINATION FOR THE DEGREE OF BACHELOR OF
COMMERCE
CMS 300: OPERATIONS RESEARCH II- SUNDAY CLASS
DATE: DECEMBER 2010 TIME: 2 HOURS
INSTRUCTIONS: Answer question ONE and any other TWO questions
QUESTION ONE
(a) In Kitale 90% of all sunny days are followed by sunny days and 80% of all cloudy days are
followed by cloudy days. Use this information to model Kitale’s weather as a Markov
chain. Indicate whether the chain is ergodic. [4Marks]
(b) Consider the following transition matrix
0 0 1 0 0 0
0 0 0 0 0 1
0 0 0 0 1 0
P = ¼ ¼ 0 ½ 0 0
1 0 0 0 0 0
0 1/3 0 0 0 2/3
(i) Which states are transient? Explain [4Marks]
(ii) Which states are recurrent? Explain [4Marks]
(iii)Which states are closed? Explain [4Marks]
(c) With the help of examples, distinguish between programmed and nonprogarammed decisions
[6Marks]
(d) Distinguish between classical and behavioural decision making models [8Marks]
QUESTION TWO
(a) A maize and beans farmer sells his final harvest in tins measuring 250 grammes. He sells the
maize and beans in this measure at Kshs 10 and Kshs 12 respectively. He wishes to determine his
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optimal solution. Your classmate implemented his problem in solver but when printing out, the
printer ran out of ink. Part of the solution follows.
(i) Compute the values in the shaded cells [2Marks]
(ii) Set up the farmers optimization problem [5Marks]
(iii) Determine the formulas used in cells C6, C8, C9 and C10 [6Marks]
(b) The failure rate of 10 bulbs in a house are summarized below
END OF MONTH 1 2 3 4 5 6
PROBABILITY OF FAILURE 0.05 0.2 0.4 0.65 0.85 1.00
The cost of replacing an individual bulb is 45/=. If all bulbs are replaced, the cost will be 32/=
per bulb. Determine the cost of individual replacement policy [7Marks]
QUESTION THREE
Coca Cola Kenya market survey has revealed, Kenyans use Coke and Fanta flavours most. The survey
has further noted that given a person last purchased Coke, there is a 90% chance that her next purchase
will still be Coke. Given that a person last purchased Fanta, there is an 80% chance that her next
purchase will still be Fanta.
(a) If a person is currently a Fanta purchaser, what is the probability that she will purchase Coke
three purchases from now. (5 Marks)
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(b) If a person is currently a Coke purchaser, what is the probability that she will purchase Coke
three purchases from now. (5 Marks)
(c) Suppose each customer makes one purchase of her brand during any week (52 weeks = 1 year).
Suppose there are 10 million coca cola product purchasers. Suppose one fanta/coke cost $1
to produce and is sold for $2. For $50 million, an advertising firm guarantees to decrease
from 10% to 5% the fraction of coke customers to switch to fanta after a purchase of coke.
Should the subsidiary that makes coke hire the advertising firm? (10 Marks)
QUESTION FOUR
Think of a practical network application and demonstrate how you can generate the optimal solution
for the shortest routing. Explain all the steps. [20Marks]
QUESTION FIVE
KCA University plans to connect an underground optic fibre to its nine buildings. In an effort to
minimize on cable length, management would like to determine the shortest routing between locations.
The following network shows path roads between buildings along which the fibre is to be laid.
Distances are in hundreds as tabulated.
Where distances between various nodes are
1-2 1-3 1-4 1-5 2-3 2-7 3-4 3-6 4-5 4-6
8 13 15 10 5 15 6 5 4 3
5-6 5-9 6-7 6-8 6-9 7-8 7-10 8-9 8-10 9-10
9 12 4 2 5 4 4 5 7 5
a) Formulate an LP model to determine the route a driver should take from location 1 to location
10. [12Marks]
b) Determine the relevant LINGO input for solving the model [8Marks]
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Operations Research Ii Question Paper

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