decision mathematics (jan 2011)

7/24/2019 Decision Mathematics (Jan 2011)

1/30

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

SULIT


2/30

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

SULIT


3/30

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

SULIT


4/30

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

SULIT


5/30

eNo.:

MTE

3104

Alf

of

the

foflowing

graphs

are

trees

except

(A)

Y

+

(B)

(c)

(D)

SULIT


6/30

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

SULIT


7/30

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)

SULIT


8/30

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

SI.'LIT


9/30

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

SULIT


10/30

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)

SULIT


11/30

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

SULIT


12/30

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

SULIT


13/30

;

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


14/30

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

SULIT


15/30

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


16/30

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


17/30

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

SULIT


18/30

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


19/30

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


20/30

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

SULIT


21/30

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

SULIT


22/30

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

SULIT


23/30

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

SULIT


24/30

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)

SULIT


25/30

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

SULIT


26/30

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

SULIT


27/30

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


28/30

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


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


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

decision mathematics (jan 2011)

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