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Cms 300: Operations Research Ii (Weekend Class) Question Paper
Cms 300: Operations Research Ii (Weekend Class)
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: OPERATIONS RESEARCH II (WEEKEND CLASS)
DATE: APRIL 2009 TIME: 2 HOURS
INSTRUCTIONS: Answer question ONE and any other TWO questions
QUESTION ONE
Write brief notes on the following
(a) (i) Modeling approach to decision making [5 Marks]
(ii) Benefits of modeling [5 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) A company can produce Q units of a product if K units of capital and L units of labour are
used. Capital can be purchased at Kshs 40.00 and labour at Kshs 10.00 per unit. A total of
Kshs 80.00 is available to purchase capital and labour. Set up the optimization problem.
[3 Marks]
(d) Define dynamic programming problem. State and explain any three applications of dynamic
programming [7 Marks]
QUESTION TWO
Consumer Watch carried out a research by collecting data from1000 shoppers to Uchumi and Ukwala
stores over a 2 week period to determine customer loyalty. The findings showed that shoppers who
shopped at Uchumi in week 1, 90% of these shoppers shopped again at Uchumi in week 2 while the
remaining 10% switched to Ukwala in that week 2. But for shoppers who shopped at Ukwala in week
2
1, 80% of these shoppers shopped again at Ukwala in week 2 while the remaining 20% shifted to
Uchumi.
a) Set up the transition matrix for these findings [4 Marks]
b) Compute the steady state probabilities if you are told that 1 ? represent probability that
shoppers will go to Uchumi and 2 ? probability that shoppers will go to Ukwala stores
[6 Marks]
c) If 2 ? increased by 0.5 and if you are told that the average weekly profit per customer is 65 by
how much will Ukwala’s profit increase? [4 Marks]
d) Demonstrate your understanding of the Minimum spanning tree problem [6 Marks]
QUESTION THREE
Suppose the economy has two sectors, agriculture and industry, where each unit of gross output of
agricultural products QA requires inputs of 0.2 units of agricultural products and 0.3 units of industrial
products. If each unit of gross output of industrial products QI requires 0.1 units of agricultural
products and 0.4 units of industrial products:
(a) Find an expression for gross agricultural output [2 Marks]
(b) Find an expression for gross industrial output [2 Marks]
(c) Find an expression for QA and QI [10 Marks]
(d) Find the required gross output when final demand for agriculture and industry respectively are
given by YA = 200,YI = 600 [6 Marks]
QUESTION FOUR
a) KCAU IT department is installing an electronic mail system in its main campus at Juja. The
following network shows the possible electronic connections between its eight offices. Distances
between the offices are in hundreds of meters. Design an office communication system that will
enable all offices to have access to the electronic mail service. What is the minimum length of the
connections that will be needed to install the mail system?
[4 Marks]
3
3
2
2 0.5 1.5 1
3 1 2.5
1.2 0.5 3
1.6 1 4
4
b) Use the shortest route algorithm to find the shortest route from node 1 to each of the other nodes in
the following network. Numbers on arcs are distances in meters. Show all your working.
[6 Marks]
5
7
6
9 4
2
18 3
3
(c) Formulate the LINGO LP model for the network provided in (b) above [10 Marks]
QUESTION FIVE
a) The failure rate of 600 street bulbs 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 35/=
per bulb. Determine the cost of individual replacement policy [10 Marks]
1
2
3
4
5
6
7 8
1
3
2
4
5
6
7
4
b) Exhaustively interpret the following LINGO output for a shortest path problem [10 Marks]
Global optimal solution found at iteration: 0
Objective value: 8.000000
Variable Value Reduced Cost
X12 0.000000 0.000000
X13 1.000000 0.000000
X24 0.000000 0.000000
X25 0.000000 0.000000
X35 1.000000 0.000000
X46 0.000000 0.000000
X56 1.000000 0.000000
X22 1.000000 0.000000
X33 0.000000 0.000000
X44 1.000000 0.000000
X55 0.000000 1.000000
Row Slack or Surplus Dual Price
OBJECTIVE 8.000000 -1.000000
FROM_1 0.000000 -6.000000
FROM_2 0.000000 -2.000000
FROM_3 0.000000 -3.000000
FROM_4 0.000000 1.000000
FROM_5 0.000000 1.000000
T0_2 0.000000 2.000000
T0_3 0.000000 3.000000
T0_4 0.000000 -1.000000
T0_5 0.000000 0.000000
T0_6 0.000000 -3.000000
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