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Hbc 2239: Operation Research Ii Question Paper
Hbc 2239: Operation Research Ii
Course:Bachelor Of Commerce
Institution: Dedan Kimathi University Of Technology question papers
Exam Year:2013
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DEDAN KIMATHI UNIVERSITY OF TECHNOLOGY
University Examinations 2013/2014
SECOND YEAR FIRST SEMESTER EXAMINATION FOR THE DEGREE OF BACHELOR
OF COMMERCE
HBC 2239: OPERATION RESEARCH II
DATE: APRIL 2013 TIME :2HRS
Instructions:
1. Answer QUESTION ONE and any other TWO QUESTIONS.
2. Show clearly your work and the number of questions attempted.
QUESTION ONE (30 Marks)
a) In a linear programming problem the objective function and constraints were
determined to be as follows.
Maximise Z= -x1-x2+3x3-2x4 Profit
Subject to:
x 3x - x 2x 7 1 2 3 4 ? ? ? Resource A
- x - 2x - 4x 12 1 2 4 ? Resource B
- x 4x 3x 8x 10 1 2 3 4 ? ? ? ? Resource C
Where xj ? 0 , j=1,2,3,4
i) By simplex method find the final table. [7 Marks]
ii) Give the optimal solution and the value of the corresponding objective function
[3 Marks]
iii) For the variable x2, give an interval for their objective function coefficient such that
the present basic solution remains optimal. [4 Marks]
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b) The national park service plans to develop wilderness area tourism. Four allocations
in the area are designated for automobile access. These sites, and the distances (in
KM) between them are listed in the table below. To inflict the least harm on the
environment, the park service wants to minimize the miles of roadway required to
provide the desired accessibility. Determine how roads should be built to achieve
this objective.
Park
Entrance
Wild Falls Majestic Rock Sunset Point The Meadow
Park Entrance - 7.1 19.5 19.1 25.7
Wild Falls 7.1 - 8.3 16.2 13.2
Majestic Rock 19.5 8.3 - 18.1 5.2
Sunset Point 19.1 16.2 18.1 - 17.2
The Meadow 25.7 13.2 5.2 17.2 -
[7 Marks]
c) Define the following terms giving examples
i) Cyclic chain. [3 Marks]
ii) Absorbing state. [3 Marks]
iii) Steady state. [3 Marks]
QUESTION TWO (20 Marks)
a) Three industries, packaging P, Bakery B, and Flour F are related with the
intermediate demand matrix below.
Output industry
Input Industry
F 0 . 1 0 . 2 0 . 6
B 0 . 2 0 . 6 0 . 2
P 0 . 5 0 . 1 0 . 1
P B F
The final demand for P, B and F are:
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D =
? ? ?
?
?
? ? ?
?
?
50
20
20
i) Determine the total output for products of industries P, B and F. [10 Marks]
ii) Comment on the total output for industries. [3 Marks]
b) Briefly but clearly explain the purpose of Input- Output analysis. [4 Marks]
c) What is sensitivity analysis on the objective function coefficients? Differentiate this with sensitivity
analysis on the right hand side (RHS) constants [3 Marks]
QUESTION THREE (20 Marks)
a) In brand switching between different toothpastes named Closed-up CU, Colsgate
CG and Aquas-fresh AF, the state transition matrix below is obtained for a
particular month.
From
To
? ? ?
?
?
? ? ?
?
?
0 .1 0 .2 0 .7
0 .2 0 .7 0 .1
0 .5 0 .45 0 .1
AF
CG
CU
CU CG AF
i) If the market share for the different toothpastes were 0.4, 0.3 and 0.3 for CU, CG
and AF for January 2002, what will be the market share in February 2002 and
March 2002? [6 Marks]
ii) What is the market share equilibrium situation? [4 Marks]
b) Find the optimum integer solution to the following integer programming problem
Maximize 1 2 Z ? x ? x
Subject to: 2 4 1 2 x ? x ?
6 2 9 1 2 x ? x ?
Page 4 of 4
0, 0 1 2 x ? x ? And are integers
[10 Marks]
QUESTION FOUR (20 Marks)
The following are the capacities of the water system network in Rongai town.
? ? ? ? ? ? ? ? ? ? ? ?
?2,4? 7 ?2,5? 3 ?3,5? 4 ?4, ? 4 ?5, ? 4
,1 5 ,2 11 ,3 5 1,2 2 1,4 3 1,7 6
? ? ? ? ?
? ? ? ? ? ?
C C C C T C T
C s C s C s C C C
Sketch the network and find the maximum flow and the corresponding capacity of
the minimum cut. [20 Marks]
QUESTION FIVE (20 Marks)
a) Explain the value of sensitivity analysis is linear programming problems and show
how dual values are useful in identifying the price worth paying to relax constraints
[3 Marks]
b) One of the properties (assumptions) of linear programming is that fractional values
of the decision variables are permitted, that is, divisibility. However, fractional
values might sometimes be meaningless.
i) Explain one case where fractional values might be meaningless. What
approach should be used to over-come this assumption? [2 Marks]
ii) Explain the connection between the following:
a) Reduced costs column and the range of optimality. [3 Marks]
b) Dual prices and the range of feasibility. [2 Marks]
c) Using the algorithm for cyclic networks find the shortest route from node 1 to node
6 [10 Marks]
10
1
2
3
4
6
6
5 5
7
9
3
5
5 5
9
9
6
5
10 15
12
14
10
3
13
4
2
3 7
4
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