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Code
No.:
MTE
3104
SECTION
A
(20
marks)
Answer
all
the
questions.
1- A search s carriedout by checking
very
tem
n
a list,
one
at a time,
and
without
umping,
untilthe
desired
one
is
found.
This
search
aigoiiihm
s
(A)
quick
search
algorithm.
l
B)
linear
search
algorithm.
(C)
binary
search
algorithm.
(D)
indexed
sequential
eaichafgorithm.
2.
The
purpose
of
a
search
s
to
ocate
he
number
10
n
the
list
1,
4,
8,9,
1
3,
15,16,
2A
Procedure
i.
Forming
he
ist
ii.
Find
he
middle
umber
iii, Reducehatfof the is t
Name
he
algorithm
used
n
the
above
search.
(A)
Tree
Searching
(B)
Binary
Search
algorithm
(C)
Linear
Search
algori thm
(D)
Indexed
Sequential
Search
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Code
No.:MTE
3104
3.
X-Zy
=
g
'
Fignrre1
--i
Refering
o Figure 1, determine
he regionwhich
satisfies he ineQualities
x+y )8 'ar$
2x-2y {.
(A)
|
(B)
rl
(c)
rl
(D) rv
x+y= 8
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4.
Code No.:
MTE 31Ot
Figure
2
:
lf
P
=
7x
+
4y is
the
objective
unction,
what
s
the
minimum
aiue-6i
p
over
the
easible
egion
R
in Figure
2_
tA)
(B)
(c)
(D)
40
41
5B
M
5.
There
s
a simple
connectedgraph
which
have
5
vertices,
7
edges
and
order
of each
vertex
s2,
3
or
4. The
sum
of
the
orders
of these
vertides
of
graph
s
(A)
e
(B)
12
(c)
14
(D)
16
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CodeNo.: MTE 3104
6. Each
of
the
graphs
n Figure3 has
our
vertices
and
the
same
numberof
edges-
AI T \ \D
DBc
Graph
Q
o(
| \"
AlaE\- \c) '
:
Graph R
.
Figure
3
Which
of
the two
graphs
are equivafent?
(A)
F and R
(B)
Q
and S
(C)
Pand
S
(D) Q and R
Graph S
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eNo.:
MTE
3104
Alf
of
the
foflowing
graphs
are
trees
except
(A)
Y
+
(B)
(c)
(D)
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8.
Code
No.: MTE
3104
Figure4isagraph.
A
Figure
4
DBAEC
s a
(A)
trail
(B)
path
(C) walk
(D)
cycle
9.
Table
1
shows
a
distance
matrix
of 6
townsmeasured n
kilometers.
Use
Prim'salgorithm
the towns.
(A) 62 km
(B)
65
km
(C)
67
km
(D)
70 km
Table
1
to find
the least
amount of cable needed
to
eonnect
al l
A
B
C
D E F
A 19 13
12
B 19
20
C
13
15
14
D
12 2A
15
10
12
E
10
F
14
12 B
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Code
No.:
MTE
31@t
10.
Refer
o
network
n
Figure
S_
By
uging
Kruska|s
lgorithm,
hich
of
the
ortowing
s
a
minimarspanning
t ree?
'.v"v ' t r '
' v
'i
5D12
Figure
5
--tl \
u
. I \
L
(B)
(c)
(D)
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No.:
MTE
The
stages
n a
critical
path
analysis:
prepare
he network,
draw
the
network
analysis
and
analYze
he
network-
In drawing
he
network,
which
of
the
following
tatements
s not
true?
(A) Activities are representedby arcs.
(B) Events
are
represented
by
nodes-
(C)
One
node
is
used
for
the whole
pro,iect'
tD)
Dummy
activity
s used
to modelthe
precedencescorrectly.
The
activities
of
a
project
are
isted
below'
Activity
Frecedinq
Activitv
A
B,C
D
E
F
A
B
c
D,E
Which
activity
has
to
be cornpleted
irst before
activity
B and
C can
start?
(A)
A
only
(B)
D only
(C) o ano'r
(D)
A, D,
E and
F
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Code
No_:
MTE
3104
13'
Figrre
6
shows
a
network
with
ncomplete
arfiest
nd
atest
imes.
The
uration
or
each
activity
s
shown.
r-T-l
f).
--*b
_-8-}
:t{*
Find
the
value
of
X.
(A)
7
(B)
11
(c)
le
(D)
27
l-T,
I
-+-rO
t0
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Code
No-:
MTE
3104
14-
Figure
7 shows
a cascade
chart-
which
of the
foilowing
are
true?
Figure
7
t.
Activities
C, E,
F are
critical
activities.
ll-
The
project
an be compreted
n
a minimum
of
six weeks.
ll.
Activities
A,
B, D
and G
can
float in
a
minimum
of
six
weeks.
lv.
Activity
c
precedes
D,
and
can
start
at any
time
during
he
first
week.
v.
Activity
E
precedes
F, and
can
start
at
any time
during
he
third
week
(A)
l,
l l and,V
only
(B)
l,
l l
and lV
only
(C)
l, l l l
and
lV
only
(D)
lt, V
and
V
only
l l
Duration
{\.reks)
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Code
No.:
MTE
3104
15'
The
lowchart
n Figure
Sdescribes
n
algorithm-
he
function
nt(y)
means
the
ntegerpart
of
y
obtained
y roundinglt
owards
O.
What
s
the
output
of
(A)
"Reject",
0
(B)
'Accepr",
O
(C)
"Reject",
50
(D) 'Accept",50
the
above
algorithm
f
x
=
SA?
y=xl5
l2
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Code
No-:
MTE
3104
16.
Algorithm
an
becommunicated
n
various
ways.
Choose
he
suitable
ways.
t.
Flowcharts
ll.
PseudoGode
l1l.
Written
English
lV.
Structure
diagrams
(A) l , l land
l l lon lY
(B)
ll, lll,
and
V onlY
(C)
lll,
lV and
lV onlY
(D) l,
l l , l l
and
V oniY
17.
A
carpenter
as
ptanks
of
10
meters
n length-
He wishes
o cut
the lengths
of
the
plank
according
o
the
order
of sale
he
received:
Length(m)
Number
35
44
26
69
73
His strategy
S
o
search
or
combinations
y adding
up
to 10
meters
and
then
cut
the
planks
according
o
the combinations-
What
type of
algorithm
has
the
carpenter
pplied?
(A)
First-fii
algorithm
:
(B)
Full-bin
lgorithm
(C) Combination lgorithm
(D)
First-f itdecreasingalgorithm
l3
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;
Code No-: MTE3104
18-
Elevenboxes are
packed
nto
each
crateswhich
has a weight
imitof 100 kg.
The boxes
(weight
n kg) n
its original
arrangement re
as
shown
60,50,40, 50,20,40,30,30, 30,40
. By applying the first it algorithm o the problem,what wouldbe the resulting
packing?
(A)
(B)
(c)
(D)
l {
30
20
4A 50 30 30
60 50 40 4A
Grate
1
2 3 4
30 40
40 50 40 30
60 50 2A
30
Crate
1 2 3 4
20 30
40
50 40
30
60 50 40 30
Grate
I
2 3 4
30
40
40 50 30 40
60 50 30 20
Crate
I
2
3 4
s{.J *tT
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24.
Code
No.:
MTE
3104
19-
Table
2 shows
a
list
of
6
numbers'
(A)5.7e132.86
(B)75e13286
(cI
7e513286
(D)97513286
t\
Pass
Order
0
8
6
3
5
I
2
Table
2
lf
an interchange
sort
aigorithm
s applied,
which
of
the following
is
the
order
of
the numbers
afier
ihe
fourth
pass?
(A)
2,3,5,6,9,
8
(B)
2,3,6,5,
9, I
(c)
2,3,5,6,8,9
(D) 2,6,3,5, 9, B
9,7,
6,
13,2,
B,
6, .16
Figure
9
By
using
Shuttle
Sort
Algorithm
o
the
list n
Figure
9, rearrange
he following
numbers
nto
ascending
order.
What
is the
rdsult
at
the
end
of
the
third
pass?
16
16
16
16
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CODE
NO.
MTE 31
04
INDEX
NO.:
SECTION
(40
marks)
Answer
ll
the
questions.
1
(a)
(i)
Sketch
a
graph
with
he
oltowing
roperties:
Order
of vertex
1
2
3
4
Number
oi
vertices
z
1
2
1
(ii)
(2 marks)
(3
marks)
(5
marks)
st-it_tT
(b )
Write
down
the incidence
niatrix
or
the
graph
above
Sketch
a
tree
with the
followingproperties:
Order
of vertex
1
2
3
4
Number
of
vertices
6
1
0
2
to
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ODE
NO. : MTE
3104
(a)
State
four
INDEXNO.:
necessary
stages n applying
Kruskal'salgorithm
o
a
network.
Stage
1 :
Stage2:
Stage
3:
Stage
4 :
(4
marks)
(b)
UseKruskal's
lgorithm
o find
he
minimum
panning
ree
or
the
weighted
raph
n
Figure10.
D
Figure10
B
4
C
F
5
E
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3.
CODE
NO.:
MTE
3104
INDEX
NO.:
The
activitynetwork
n Figure
11
shows
he
duration
in
weeks)
of
seven
activities
of a
building
project,
and
their
precedent
activities.-
List
he
activities
hich
must
start
and
inish
on
no
delay
n
the
project.
Figure
11
(a)
Complete
he
network
their
earliest
nd
latesl
Figure
11
above
by
itling
start
ime.
in
lhe
events
complete
with
(7
marks)
t ime
to
ensure
here
s
')
b)
(ii
)
What
"
tf,*
minimum
ime equired
o
complete hisproject?
(2
marks)
(1
mark)
A(12)
r(1
)
c(13)
1q
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CODENO. : MTE3104
INDEX
NO.:
4. Below s a list of number
7,9,5,1,11,3
Apply bubblesort
algorithm
o
sort
the list
of numbersabove n ascenciing
order and
the results n the
Table 3 below-
Table 3
(10
marks)
Originallist
7
I 5 1
11
3
Numberof
swaps
After
irst
pass
After second
pass
After third
pass
After fourth
pass
After fifth
pass
19 SULIT
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CODENO.
: MTE3104
SEGTION
G
(40
marks)
Answer
any two
questions.
1. A furniture actory produces wo types of chair: plasticchair and wooden
chair
for children. All
the chairs
have lo
pass
through
machine A
and
machine
B
for
quality
inspection.
A
plastic
chair requires
3
minutes
on
machine
A and
2 nrinutes
n machineB.
A wooden
chair
equires
minutes
on
machineA
and I
minuteson machine
B- Each
machine
an
be used
for
a
maximuni
of
60 hours in a week-
The
material
ost or
a
plastic
chair
s
RM
10.00
and
for an
wooden
chair
is
RM
8.00.
The
overhead
costs
are RM
5000.00
per
week-
The factory
sells
each
plastic
chair
and wooden chair
at
RM 20.00
and RM
25.00
respectively.
he
factory
wishes o
maximize ts weeklyeamings.
Apply the
simplex
method
to determine
the
number
of
plastic
chair
and
wooden
chair o
be
produced
per
week
to
maximize
profit.
What
s
the
amount
of
the
maximum
rofit
per
week?
Give one
reason
why he
simplex
method
s
used
rather
than
the
graphical
method in
solving
certain
programming
problems.
(20
marks)
2A
st
iLt i
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CODENO. :
MTE 3104
2-
Manisah's family
is heading
owardsGombak
Setia when
they notice hat
the
cars
ahead of
them
have come
to a complete
standstill because of an
accident.They
stopped
at
the road
side of main
road
and
consult he map-
The network n Figure
12
represents
he roads
that his
family
can use
to
get
from the site of the accident (A) to Gombak Setia (G). The length of each
section of
the road is shown
in kilometres-
Dijkstra's algorithm
can
be used
o find the shortest
route rom
A to G.
Apply
Dijktra's
algorithm
on a copy
of the figure
to
find
the shortest
route from A
to G. Show
allyour working
clearly,and
indicate
he
order
in
which to
assign
permanent
abels o
the nodes.
(13
marks)
Use Kruskal's
algorithm
o find
a minimumconnector or
the network
n
Figure
12. Draw
he minimal
panning
ree and
find the lengthof
the
minimuinconnector.
(7
marks)
(a )
(b)
21
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CODE
NO.
MTE
3104
3.
Table
4
befow
gives
he duration
of
the
activities
nd
heir
mmediate
predecessors
f
a
construction
project.
Activity
Duration
days)
lmmediate
redeccessors
A
1
B
2
C
3
A
D
2
A,B
E
3
D
F
4
C,E
fable
4
(a)
construct
an
activity
network
o illustrate
he
above
nformation_
(10
marks)
(b)
Perform
fonruard
ass
and a
backward ass
o find
the
earliest
and
latestevent times.Find he criticalpath ndcalculatehe minimum
time
of
completion.
(10
marks)
@
Government
of
Malaysia
2O11
22
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CodeNo.:
MIE
3104
SECTION
/o^ -^rkah)
.
\LV
ttta
1.
B
2.8
11.
C
12.
A
13.
C
14.
D
15.
B
16.
D
17. B
18.
B
19.
A
20.
c
D
D
r-
C
C
B
A
t]
Each
correct
answer
=
1 mark
10x1mark=l0marks
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Code
No.:MTE
3104
'
-AnsWer
all the'questionS
1.
(a)
( i )
SECTION
B
(40
marks)
-
, , . .
- . . . -- . , : . . .
Accept
any
oJher
correct
graph
6
vertices
of
order
1
1
vertex
of order
2
2 vertices
of order
4
A2
PMM
(ii)
A1
A1
A1
(b)
AII correct
A5
Minus
I
mark
for
every
mistake
Total
=
[10
marks]
A B
C
D
A
2
1
1
0
B
1.
0
1
2
c
1
1
0
2
D
o
2
2
0
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Code
No-:
MTE
3104
PMM
2.
1.
Choose
he shortest
edge
(if
there
is
more
han
one,
choose
any
{a)
2.
3.
4.
of
thg-sho.rtg.st: . , j : .
. : . ' -
: . . . , : . . . .
. . :
: . . : - . .
: . , - . . . . .
Choose he next shortestedge and add it
Choose
he
next
shortest
edge
which
wouldn'tcreate
a cycle
and
add
t.
Repeat
untillwe
have
rninimal
panning
ree.
(
4 marks
)
Minimum
spanning
ree
=
17
5 marks
1
mark
Total
-
[10
marks]
(b)
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Code No.:
MTE
3104
3.
a)
Diagram
8
(a)
Both
pairs
of the
earliest
start
time
and
the
latest
start
ime
correct
except lrToI
{6xl
mark)=
M6
All the eventsconecfly numbered
(b)
(i)
A,
D,
E,
G, I
Minus
1
mark
for
each
mistake
(ii)
56
weeks
Total
=
10
marks
A1
M2
A1
PMM
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Code
No,:
MTE
3104
4.
Ditn,
I tvt
tv l
Each
row of
the sorted
result correctly
done.
=
(5
x 1 mark
=
5 marks)
(Start
rom
second
pass,
accept
ollow
hroughanswers)
Number
of swaps
or each
sorting
conectly
ecorded.
=(Sxl
mark=5marks)
Total=
10
marks
7
9
5
1 11 3
Numberof
,,
s.{.QPs
After
irst
pass
1
5
1
I
J
11 3
After
second
pass
5
1 7 3
9
11
J
After
hird
pass
1 5
3
7 9
11 2
After
ourth
pass
1 3
5
7 I
11
1
After
ifth
pass 1
3
5
7
I
11
0
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Code
No.:
MTE
3104
Maximize
Subject
o
Maximize
Subject
o
The
simple
ableau
Introduce
wo
slack
variables
and v
So,
the
standard
orm
SECTIONC(40marks)
f
=
(2a_:10)x
(25
.g)t
_
5000
3x+
2y
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f X
v
U
Solution
Ratio
Test
f
1
-23t4 0 0
17lB
2650
u
0
512
0
1
114 2740 270O=512=1OBO
v"
a'-
'
114'
'1
' -
0
1/B
..
450
456
-
114'=
800
No.:
MTE3104
Answer: Maximum
value
of
P
=
8860
'x
=
1080
y
=
180
PMM
Determine
pivot
row
=
(1
mark)
Correct
ivot
element
=
(1
mark)
Rr
(all
correct)
=
(1
mark)
Rz
(all
correct)
=
(1
mark)
R2:512
=
(1
mark)
R2all
entries
orrect
=
(1
mark)
-
(1
mark)
=
(1
mark)
=
(1
mark)
One
eason:
Simplexmethodcan be used o solve inearprogramming rogram
'
with
3
variablesor more-
=
(2
marks)
Total
=
20 marks
t
X
v
U
Solution Ratio
Test
f
1 -2314
0
0
1718 2650
u
0 1
0
2t5
'
-1t10
1080 Rz:512
V
0 114
I
0 1tB 450
f
X
v
U
Solution
Ratio Test
t
1 0
0 2311031120
BB60
U
0 1
0
215
-1nA
1080
001-11103120 180
SULIT
7/24/2019 Decision Mathematics (Jan 2011)
29/30
Code
No.:
MTE
3104
(a)
.
(b)
5
outofseven
spaces
correcilyfiiled
up
Shortest
ength
=
47
km
Use
Kruskal's
algorithm
corecUy
to
find
the
All arcs correcfly drawn.
Total
minimum
connector
=
B0
6x
2mark=lZmarks
I
mark
Sub
Total
=
13
marks
G;
minimum
ength
6Xl mark= 6marks
1
mark
SubTotal=Tmarks
Total
=
20
rnarks
PMM
A
sl36
J(]
1
I
0
0
2 20
20
47
47
12
D
SULIT
7/24/2019 Decision Mathematics (Jan 2011)
30/30
3 (a)
Code
No.:
MTE
3104
PMM
Network
and
arrows
drawn
and
activities
abelled
correctly.
Network
explicitly
rawn
(4
marks)
Activities
orrectly
laced
(4
marks)
Arrows
drawn
(2
marks)
(b)
1
mark
or
each
pair
of correct
earliest
and
latest
event
ime
(6marks)
Critical
ath
(1,2\----(2,41--(4,$
----(5,
6)
Minimum
ime
of
comPletion
11
daYs
(4
marks)
Total
:20
Marks
@Govemmentof MalaYsia20ll