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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:2009
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UNIVERSITY EXAMINATIONS: 2009/2010
THIRD YEAR STAGE I EXAMINATION FOR THE DEGREE OF
BACHELOR OF COMMERCE
CMS 300: OPERATIONS RESEARCH II (SUNDAY CLASS)
DATE: DECEMBER 2009 TIME: 2 HOURS
INSTRUCTIONS: Answer question ONE and any other TWO questions
QUESTION ONE
a) CMC Auto manufactures luxury cars and trucks. The company believes that its most likely
customers are high-income-women (HIW) and high-income-men (HIM). To reach these two
groups, CMC Auto has embarked on an ambitious TV advertising campaign and has decided to
purchase one (1) minute commercial spots on two types of programs: comedy shows and football
games. Each comedy commercial is seen by 7 million HIW and 2 million HIM. Each football
commercial is seen by 2 million HIW and 12 million HIM. A 1-minute comedy advert costs Kshs
50,000.00, and a 1-minute football advert costs Kshs 100,000.00. CMC Auto would like the
comedy and football commercials to be seen by at least 28 million HIW and 24 million HIM
respectively. CMC Auto wishes to determine how it can meet its advertising requirements at
minimum cost
(i) Determine the decision variables [3 Marks]
(ii) Set up the objective function [3 Marks]
(iii) Set up the constraints facing CMC Auto [6 Marks]
b) The distances (in kilometers) between the cities Alpha, Beta, Gamma, Delta and Epsilon are
tabulated below. A road system has system has to be built to connect these cities. For political
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reasons, no road can be built connecting Gamma and Epsilon and no road can be built between
Alpha and Beta.
City Alpha, Beta, Gamma, Delta Epsilon
Alpha - 132 217 164 58
Beta 132 - 290 201 79
Gamma 217 290 - 113 303
Delta 164 201 113 - 196
Epsilon 58 79 303 196 -
Use Minimum spanning tree algorithm 2 to determine the connections between the cities that will
minimize the total length of roads to be built. Show the connections and give the total length. Explain
all your steps [18 Marks]
QUESTION TWO
Write brief notes on the following three. Include illustrations in your descriptions.
a) Shortest route problem [7 Marks]
b) Minimum spanning tree problem [7 Marks]
c) Maximum flow problem [6 Marks]
QUESTION THREE
A market study collected data from 1000 shoppers over a 10 week period invoving two chain
supermarkets, Uchumi and Ukwala. These data show of all the customers that shopped at Uchumi in a
given week 90% again shopped at Uchumi the following week, while 10% switched to Ukwala and of
all the customers that shopped at Ukwala in a given week 80% again shopped at Ukwala the following
week, while 20% switched to Uchumi.
a) Define a Markov chain [3 Marks]
b) State any three examples of the Markov process [3 Marks]
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c) Assume state 1 represent a customer shopping at Uchumi and state 2 represent a customer
shopping at Ukwala. Determine the probability of the system ending in state 1 and state 2
respectively. [8 Marks]
d) Suppose Ukwala is contemplating an advertising campaign to attract more of Uchumi’s
shoppers. Ukwala believes that this promotion strategy will increase the probability of Uchumi
shoppers switching to Ukwala from by 5%. Determine the steady-state probabilities
[6Marks]
QUESTION FOUR
A machine tool company conducts a job-training program for machinists. Trained machinists are used
as teachers in the program at a ratio of one for every ten trainees. The training program lasts for one
month. From past experience it has been found that out of ten trainees hired, only seven complete the
program successfully (the unsuccessful trainees are released). Trained machinists are also needed for
machining and the company's requirements for the next three months are as follows:
January 100
February 150
March 200
In addition, the company requires 250 trained machinists by April. There are 130 trained machinists
available at the beginning of the year. Payroll costs per month are:
Each trainee 400
Each trained machinist (Machining or teaching) 700
Each trained machinist idle (Union forbids firing them) 500
Set up the linear programming problem that will produce the minimum cost hiring and training
schedule and meet the company's requirements. [20 Marks]
QUESTION FIVE
a) Explain the transactions table of the Input output model [6 Marks]
b) Determine whether the function 2
1 2 2
2
1; 2 1 f (x x ) = -x - x x - 2x is convex or concave. [10 Marks]
c) With the help of an illustration, explain a non linear problem/model [4 Marks]
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