JAWAPAN

MODUL SOLAF MATEMATIK TAMBAHAN 2014 J-39

[ 2 m / Aras T ]

x

y

x = 12

x + y = 15

3x + 4y = 240

x = 2y

300x + 350y = 10 500

R

( 48 , 24 )

10 20 O 30 40 50 60 70 80

6

10

20

30

40

50

60

70

80

1.(a) 3x + 4y 240 x 2y x + y 15 (b) graf

(c) (i) 6

(ii) RM22 800

JAWAPAN MODUL 21

PENGATURCARAAN LINEAR

KERTAS 2

JAWAPAN

MODUL SOLAF MATEMATIK TAMBAHAN 2014 J-40

x

y

x = 20

x + y = 30

5x + 4y = 300

x = 3y

R

10 20 O 30 40 50 60 70 80

10

20

30

40

50

60

70

80

2.(a) x + y 30 x 3y 5x + 4y 300 (b) graf

(c) (i) minimum = 10

maksimum = 50

(ii) RM2 800

JAWAPAN

MODUL SOLAF MATEMATIK TAMBAHAN 2014 J-41

10

x = 20

x + y = 90

y x = 10

x = 2y

R

3.(a) x + y 90 x 2y y x 10 (b) graf

(c) (i) 10 y 30

(ii) RM10 200 y

20

30

40

50

60

80

70

90

x

10 20 30 40 50 60 70 80 O

( 60 , 30 )

6x + 5y = 60

JAWAPAN

MODUL SOLAF MATEMATIK TAMBAHAN 2014 J-42

x

y

y = 10

x + y = 18

2x + y = 2

2x = y

R

2 4 O 6 8 10 12 14 16

2

4

6

8

10

12

14

16

4.(a) x + y 18 4x + 3y 48

2x y (b) graf

(c) (i) 8

(ii) RM40

18

4x + 3y = 48

18

( 5 , 10 )

JAWAPAN

MODUL SOLAF MATEMATIK TAMBAHAN 2014 J-43

50

100

150

200

250

300

350

400

450

500

225

x

y

x = 100

x + y = 500

5x + 4y = 1 400

x = 3y

R

50 100 O 150 200 250 300 350 400

5.(a) x + y 500 x 3y 5x + 4y 1 400 (b) graf

(c) (i) 225

(ii) RM7 125

( 375 , 125 )

JAWAPAN

MODUL SOLAF MATEMATIK TAMBAHAN 2014 J-44

x

y

x = 30

x + y = 170

y 2x = 20 300

R

10 20 O 30 40 50 60 70 80

20

40

60

80

100

120

140

160

6.(a) x + y 170 x + y 80 y 2x 20 (b) graf

(c) (i) 80 y 140

(ii) RM14 600

180

x + y = 80 5x + 4y = 200

( 50 , 120 )

JAWAPAN

MODUL SOLAF MATEMATIK TAMBAHAN 2014 J-45

x

y

y = 15

x + y = 20

2x + y = 40

x = 2y

R

5 10 O 15 20 25 30 35 40

5

10

15

20

25

30

35

40

7.(a) x + y 20 x 2y 2x + y 40 (b) graf

(c) RM75

JAWAPAN

MODUL SOLAF MATEMATIK TAMBAHAN 2014 J-46

5

x

y

y = 3

2x + y = 30

10x + 3y = 120

x = y

R

2 4 O 6 8 10 12 14 16

10

15

20

25

30

35

40

8.(a) 10x + 3y 120 2x + y 30 x y (b) graf

(c) RM2 700

13

JAWAPAN

MODUL SOLAF MATEMATIK TAMBAHAN 2014 J-47

x

y

x = 200

2x + y = 600 3x + 2y = 1 500

x = y

R

100 200 O 300 400 500 600

100

200

300

400

500

600

700

800

9.(a) x y 3x + 2y 1 500 2x + y 600 (b) graf

(c) (i) 120

(ii) RM3 400

450

120

JAWAPAN

MODUL SOLAF MATEMATIK TAMBAHAN 2014 J-48

x

y

x = 2y

3x + 7y = 210

5x + 3y = 300

y = 2x

R

10 20 O 30 40 50 60 70 80

10

20

30

40

50

60

70

80

10.(a) 5x + 3y 300 3x + 7y 210 y 2x (b) graf

(c) (i) RM229

(ii) 46

90

100

8x + 5y = 80

( 13 , 25 )

46