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coDrr No. : FITE 3104Malaysia 60sen

SECTION A(20 marks)

.Answer al l fhe questions.

1" [n a two person game, one player thinks of a worcJ and invites ihe othei- roguess what that word is- In response to an incorrect guess, ihe first pluy".indicates wngfe.r the mystery word is before or after the word guessed inalphabetical (dictionary) order.

Given that a-dict ionary is available, name a strategy for the second player tofollow in trying to find the word in as few guesses as possible.

(A) Quick search

i{r) Binary search {/

{C) Linear searchOf

(D) lndexed sequential search4/

,t\ teacher, Mr. Johari.Ahmad, was trying to rocate a student named Mary.JLrne. He collected a list of all the students of the school randomly. He thenchecked al l the names in the l ist in numericalorders. But he sti l l could notlocate the name Mary Jane.

Whaf tr.rne of s.e3rq[ algor-tthr-n has lr"4r. Jchei AhamC cxecuted?

(A) Linear Search htgorithm

Binary Search Algorithm ;r

Unsuccessful Search Alqorithm

(B)

{c)

(D) lndexed Sequential Search Alsorithmr,z

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oCODE NO. : N{ ' IE 3104

3. consider the fol lowing four t inear programming models. By using the

graphicatapproach,determinewhichmodel isnotbounded.

(A) Max,z = Bxt + 5xzsubject to

+ xz s B4x1 + 31r <16

(B) Max,z=x+3XzSubject to

xr +3xz384x1 +3Y' <29

(C) Max, z = 2xr +xz

Subject toXr -Xz <5

2xr <15

(D) Max,z=x+3xSubject to

X1 - 3X2 <-12

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I

. f i

COIIE NO : Ir,iTE 3104

4. Figure 1 shows a feasible region R thai satisfies a system of inequalities.

\' r \ ! ( (3a t

<(o,

utr>

,L" ;* \tcJ

oLo

\\

\r \ :\

. \

.- Figure 1

Which of the following points gives the maximum value of Sx + 6fr

(A) A

(B) B //'

i i : ; c

{D) D

The following shows some information of a simple connected graph.

Number of vertices are 6.Number of edges are gOrder of each vertex is either 2,3 or 4.

The sum of the order of the vertices is

tt '

ttL+s)

(A) 10

(B) 12

(c) 16

(D) 18 .z./

ru

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,$L1 jl

l

-. '.

-_ |

v:

CODI NO. : Iv{TE 3104

6. Al l the fol lowing graphs are trees except

(A)

iR\

(c)

/n\

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CCDE NO

7.

MTE 3I 04

I }

FigureFigure 2 shows a graph which representsWhat type of graph is this?

(A) A tree t

(B) 'Awalk ' , , ',/

(C) A cycle

(D) A digraphr'

Figure3isagraph.

4

Which of the fol lowing is a Hamiltonian cycle?

(A) EADCE

(B) CDABEG

(c) BCDEBA

(D) ABCEDEA

2the route ABCDEB.

/t

Figure 3

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I

. : ,

CODE NO. : MTE 3104

L Use Prim's algorithm to findrepresented by the matrix in

a minimum spanning tree for the networkTable 1 below.

Table 1

(A) 13

(B) 14 ,,

,/(C) 1Y

(D) 16

10.

, Figure 4

ln Figure 4, the numbers represent the length of the arcs. To find the minimalspanning tree using the Kruskal's algorithm, AB is first selected-

Which arc should be selected next?

(A) 'AB

(B) BF

(c) AE

(D) CD,//

A B D E

A o 5

"-B_ B 4A 1

I 1

l)aI o

E 3 b

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CODE NO. : l{TE 3104

11 . Vv'hich of the following statements are true about the concept of criticat pathanalysid?

. I Circles are used to represent activities in a network diagram, F

II. Dummy activities are used to modelthe precedences correctly.

llt. The critical path is a sequence of actrvities where there is no -scheduling f lexibi l i ty.

-,-i' lV, Critical path analysis is a technique to plan and monitor projectsio maximize efficiency.,

(A) ];t|andil*oilY

(B) ffit\foilf

(C) t-lltane-*my/'

(D) l l , l l land tv ontrz/-P

12. Dummy activities are used in activity network to force correct logic.which of the following precedence tables requires the use of dummy activity?

(A) Aciivity Depends onA BD A,C

I

Activity Depends on

C A,BD B

Activity Depends onD A

E B,C

{B)

t\- i

(D)

a

Activity Depends onc A,BE DF C,E

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IcCODENO. :M' fE 3104

Questiorrs 13 and 14 refer to Table 2'

Table 2 shows the duration and immediate predecessors for seven activities in a

small construction project- Each activity can be completed by one worker.

Activity A B D E F \ l

Duration(lrours)

? 1 1 .>Z 3 J

lmmediatePredecessors

A,B A C,D

Table 2

13. The minimum time for the construction project is

(A) 7

(B) e

_ /^\ 1^( \ - / rv -

(D) 12.\- )

14. The minimum number of workers required to maintain the minimum project

completion t ime is

(A) 2 .,

(B) 3

(c) 4

(D) 7

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aCODE NO. : MTE 3104

15.

( 1/

t a l

tt 4/

(s)

Figure 5

Figure 5 shows a flow chart which defines- an algorithm operating two inputs,x and y. Run the algorithm with starting inputs of x = 3 and y = 41.

How many times are the instructions Q ""u"uted before the algorithm

ends? \--l

/A\ 11\- / t

/F l \ 4 '\UI IL

(c) 13

(D) 14

Read x and y

Letr=yandq=g

Letr=r-xLetq=g+1

l0 SULIT

CODE NO. : IvITE 3104

16, Which of the following are the properties of an algorithm?

l. Each step must be defined precisely-

ll. The algorithm must work for any set of inputs.

llt. lt must produce an output and stop after afinite number ofsteps.

lV. The answer must depend only orr the inputs for a parlicularproblem.

(A) l , l l and l l lonly

(B) I, t t l and lV onfy

(C) l l , l l l , and lV only

(D) I, l l , l l l and lV only

17. Seven items with the weight giu"n in Table 3 are to be packed into as fewboxes as possible, each of whichfras a capacity of 10 kg- Three solving-methods are available. first-fit algorithm, first-fit decreasing algorithm and fullbins approach.

Item B t - D E F G

Weight, kg 6 o 4 3 3 7 2

Table 3

Which of the three methods would produce an optimal solution?

(A) Altthree

(B) First-flt only .

(C) Full bins only,

(D) First-fit decreasing and full bins only

l l SULlT

a

18. You have a number of flash drives, all with one gigabite {1GB) capacity. youare to copy the following files into some of them.

CODE NO. : h4TE 3104

File A B D E F G

Fi le s ize (MB) 900 500 700 600 100 300 204

l-;lEFIE

EET'I

E

(A)

(B)

Assume that the flash drives are able to accommodate the files to their fullcapacity, and thelr order of usage is from left to right- which of the followingpacking shows that first-fit algorithrn has been u..OZ

t"-lEEFI

En

EE

(c)

(D)

T7 SULIT

CODE NO. : MTE 3104

19. Sort the number lists given in ascending order using interchange-sort'

Which of the following is the result from the 4h pass?

tA) 2

(B) 2

{c) 2

(D) 2

20. Five numbers are listed in the following order.

Which of the following shows the shuttle sort algorithm for these numbers?

;lirt - 1't pass 2nd pass 3td pass 4th pass

(B)| 4a t r---;--'l! ' . , I I , II e l' .L_e _,1| 7 I I 15 If rs-_l [ i3 lrTil F.I

(A)

r-- --_-l! 4---ltot

I 11 IT- ^- lI rJ I

f1=_l

r--_;--l

i , lIq l

t13 lrilt 151

t- -;-1

l r llottJt

113 Ir-;-;-_-lI IJ I

l-1l_l

(c)

(D)

l1IJ

SULIT

4t.

SECTION B{40 marks}

Answer all the questions.

An incidence matrix is a way of representing the number of edges betweennodes of a graph in a matrix form. An incidence matrlx for a graph G is givenbelow.

A B C DAla 1 z 1l

t lR l1 ) 1 1t

l ' l, i , 1 0 1lDl_1 1 10J

(a) Dr,aw the graph G using the following layout.

A

I

Dc oB

i

-3

/ . - t

{ bttEmarks)

(b) Determine wether G is a Hamiltonian graph and provide a reason

(c)

14

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b. larta*ee -* \1 J-0^-

Find the Uegiee of all vertices from (a) by compteting the fol

Vertex A B C D

Degree .{ s .{ g

B C D EA I 4 IB a

I 3 4C T̂ 3 6 5D o o J

E nT 5 3

}

CODE NO.: MTE 3104

2.

INDEX NO-:

Table 4

Tabte 4 above shows a distance matrix (in km) of five post offices in a

city. Postmaster Lim is required to visit all the polst offices in one day

and he can start frorn any post office of his choice- 'i

(a) Draw the associated network for the five post offices given above.

arks)

/

/

@

15 SULIT

(b) Apply Kruskal's algorithm to heip postmasier Lim to visit all the fivepost off ices. What rs i ts minimum distance?

Irn, r f lrr li n\ rrt1\rf\ c{lS\e"n.<(

?

',.////?s

.:

S*-,- \ {z r r lo '! -\ t s + y -- (L{ br.n

! (7/marksl

rs

to SULIT

eCODE NO. : MTE 3104 ]NDEX NO.:

in Figure 6 shows activities that are involved in aThe activity duratlon is in days.

The activity networkconstruction project.

H{3}

t1l 1i

l . ! t . l )n\t+J

ci8) L(10)

(a)

Figure'b

Based on the activity diagram, complele the table below.

(b) Find the earliest project completion time and list the

iqlo hr.e is

c-rlha\ ocltvlh)es c+F-> L

/ - )-- ,( t )

(4 marks)

@^*'t

G\ry-' .t{4

B(6)

F F

K

M

17 SULIT

(c) Due to a resource probtem, activity K is detayed by 3 days. What effectwittthis have on the whole project completion time?

Y1 &* C-> F -> ( -- : M-"tf

fheeomg\e-L.vn klcna Ar- otho\a

Ft-6=F e$K

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CODE NO.: MTE 3104 INDEX NO.:

4. Appty the bubble sort algorithm on the set of numbers{26,20, 12, 17 , 32, 1A, 24} in ascending order to complete the table below.

SULIT19

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CODE NO. : MTE 3104

SECTION C(40 marks)

Answer any two questions.

1' A company manufactures two types of shampoo, A and B. The company' cannot spencr more than RMB000 as producilon cost per month. Theproduction cost for each unit of A and B are RM16 and RMB respectivelv. Themachine time required to produce one unit of A is 4 minutes and one unit of Bis 12 minutes. The machine cannot function more than B0 hours a month. Aand B each requires 6 minutes to package and the totar package timeavailable a month cannot exceed 60 hours. Profi t per unit of product A and Bare RM5 and RMB respectively.

Apply the Simplex Method to determine the number of product A and productB to be manufactured per month.to maximize profit. What is the amount of themaximum profit per month?

(20 marks)

IttIt

20 SULIT

CODE NO. : MTE 3104

Z. The network in Diagram I shows the road connections between a group of

vitlages. The numbers on the arcs represent the times in minutes that a taxi

driver takes to travel along the roads represented by those arcs. the network

is set up ready for an application of Dijkstra's algorithm-

Diagram 1

Apply Dijkstra's algorithm to find the quickest route for the taxi driver to takebetween his home in vi l lage H and his work station in vi l lage W. Show all your

working clearly, and indicate the order in which to assign permanent labels to

the nodes.

Explain brief ly how you would f ind his quickest route under thesecircumstances .

As the taxi diver is about to leave H, he hears on the radio that an accidentoccurs in the centre of village F is causin g a delay of 10 minutes to all trafficthrough that village

(20 marks)

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KerI'

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EiI.lrl i : :

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CODE NO. : MTE 3104

3. The table below shows the activities of a proiect with the precedinq activities

and the duration for each activitv-

Activity Duration(davs)

lmmediateoredecessor{s)

A 2B J

+

D 2 BE D

F 1 C.DG 6 E,F

Table 5

Draw the network diagram for the. activit ies in Table 5 complete with labeling

of activities and their duration, dummies where necessary and earliest event

time and latest event times. Determine the critical path and the shortest time

needed to complete the project. '

lf activity E is delayed by 3'days, and activity C is delaye d by 2 days,-explain

how the project is affected, if at ali. Give reasons for your answer.

(20 marksl

@ Government of Malaysia 2010

22 SULIT

,..%_8.

KEMENTERIAN PELAJARAN MALAYSIAPeperiksaanljazah Sarjana Muda Perguruan Dengan Kepujian 2010

PROGRAM IJAZAH SARJANA MUDA PERGURUAN DENGAN KEPUJIAN(MATEMATIK PENDI DIKAN RENDAH}

DECISION MATHEMATICS

CODE NO. : MTE 3104 DATE : Novemb er 2A1A

INDEX NO : 26ro)o\e qoc \tS DURATION : 2 HOURS 30 MINUTES

CENTRE : \ tG e:r l

SECTION A: OBJECTIVE ANSWER SHEET

I NSTRUCTION TO CAN DIDATES

Circle the correct response for each'question.

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@ Government of Malaysia 2010

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