Operations Research I Question Paper

Operations Research I

Course:Bachelor Of Commerce

Institution: Kenyatta University question papers

Exam Year:2007

KENYATT A UNIVERSITY
UNIVERSITY EXAMINATIONS 2007/2008
FIRST SEMESTER EXAMINATION FOR THE DEGREE OF BACHELOR OF
COMMERCE
BMS301:
OPERATIONS RESEARCH I
DATE: Thursday, 29th November, 2007
TIME: 8.00 a.m. - 10.00 a.m.
INSTRUCTIONS:
Answer question ONE and any other TWO questions.
QUESTION ONE
a)
Models plays important role in decision making. State and explain various types
of models giving examples of each.
(8 marks)
b)
State and explain areas where operation research can be applied to aid in decision
making.
(8 marks)
c)
Given the following linear programming problem and the simplex tableau below,
containing the solution to it.
i)
Formulate the dual to the given problem.
ii)
Obtain the solution to the dual from the tableau also verify that the
objective function values of both the problems are the same.
Minimize
Z = Xl + 12x2

Subject to:
6xI + 2X2 ~24
.
3xI + 2X2~ 18
XI+ 3X2~ 12
'".
XI, X2 ~ 0
Basic
XI
X2
Sl
S2
S3
Al
A2
A3
Bi
xl
1
1
0
-'lj
'lj
0
'lj
-'lj
0
2
7
8
7
8
0
0
1
-1
S3 0
-
--
--
-
8
6
3
6
3
X2 12
1
0
1
12
-1
0
--
1
0
6
12
Cj
1
12
0
0
0
m
m
m
Zj
1
1
1
1
1
12
--
--
0
-
-
0
12
6
12
6
~j
1
1
1
1
0
0
-
-
0
m--
m--
m
12
6
12
6
(14 marks)
QUESTION TWO
a)
State and explain the assumption of assignment model's
(8 marks)
b)
A Chartered Accountant firm has four Chartered Accountants each of whom can
be assigned any of the three audit assignments.
Because of the varying work
experience of the Chartered Accountants, the net surplus (professional fees minus
expenses to be incurred by the firm) varies as under:
2

Audit Assignment
Chartered Accountant
W
X
Y
A
65
78
83
B
85
52
59
C
83
56
69
D
49
80
85
You are required:
i)
To find the maximum net surplus which can be obtained
(8 marks)
ii)
Build linear programming problem model
(4 marks)
QUESTION THREE
a)
State and explain the assumption's of transportation model.
(8 marks)
b)
Sunray Transport Company ships truckloads of grains from three silos to four
mills. The supply (in truckloads) and the demand (also in truckloads) together
with the unit transportation cost per truckload, in thousand shillings, on the
different routes are summarized below:
mill
1
2
3
4
1
10
2
20
11
Silos
2
12
7
9
20
3
4
14
16
18
The supply capacity for silos 1, 2 and 3 are 15, 25 and 10 tons (000) respectively
while the demand capacities for mills 1,2,3 and 4 are 5, 15, 15 and 15 tons (000)
respectively.
Determine the minimum - cost shipping schedule between the silos
and the mills.
3

QUESTION FOUR
The following table gives the activities and other relevant data for a project
Activity
Normal Time Crash Time
Normal Cost
Crash Cost
(days)
(days)
(Shs) 000)
Shs. '000'
1-2
4
3
600
800
1 - 3
2
2
400
400
1-4
5
4
750
900
2-3
7
5
400
600
2-5
7
6
800
1,000
3-5
2
1
500
650
4-5
5
4
600
850
a)
Draw the project network and determine the normal critical path and crash critical
path.
(5 marks)
b)
Determine the standard deviation of the project completion time
(3 marks)
c)
Determine the minimum project completion time with least increase in cost over
normal cost.
(12 marks)
4

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