seafield selangor 2013 m3(a)

8/13/2019 SEAFIELD SELANGOR 2013 M3(A)

1/5

STPM 950/3 (2013)

MARKING SCHEME

No. Solution Marks

1 (a)

(i) The balance after 10 years,

08.0

108.01

10

10 xA

(ii) The balance after 20 years,

10

10

20 08.0108.0

108.01

xA

(iii) The balance after 40 years,

08.0

108.0130008.0108.01

08.0

108.01 20

201010

40 xA

08.0

108.0130008.0108.0

108.01

20

30

10

x

(b)

10000008.0

108.0130008.01

08.0

108.01 20

3010

x

82.591

1000005893.137287733.145

x

x

The value ofxis RM591.82.

B1

B1

M1A1

M1

A1

6 marks

2 (a) 2901 p

p

0109090

2

pp

pp

8

09

q

pp

Hence, equilibrium quantity is 8 units and equilibrium price is

RM9.

(b)

M1

M1

A1

A1A1

D1

D1

D1

8 marks

q

p

8

1 pq

290

p

q

0 1 9 45


2/5

STPM950/3 (2013) 2

3 (a) The initial basic feasible solution is:

0,200,120,0,04321 Zxxxx .

(b)

Basic 1x 2x 3x 4x Z Solution

2x 1 1/8 0 0 15

4x 45/4 0 -5/8 1 0 125

Z 0 0 1/2 0 1 60

Optimal solution is 60,125,0,15,04321 Zxxxx

B1

B1

B1

B2

5 marks

4 (a)

(b)

Path Total Duration (days)

A-B-D-G-H 5+8+3+4+9 = 29

A-B-E-D1-G-H 5+8+10+0+4+9 = 36

A-B-E-D2-F-H 5+8+10+0+6+9 = 38A-C-F-H 5+3+6+9 = 23

Critical path is A-B-E-D2-F-H and minimum time required is 38

days.

D3

M1

A1

B1B1

7 marks

5(a) Economic order quantity =

05.0

256002

units775

6.774

(b) Number of orders per year =775

52600

orders41

26.40

(c) Total weekly cost = 25775

60005.0

2

7756003

= RM 1838.73

M1

A1

M1

A1

B2M1

A1

8 marks

A

B

C

D3

24 7

E10

3

8

6

3

F

5

G

4

6

18

5

H

9

D1

D2


3/5

STPM950/3 (2013) 3

6

614

153

(a) Minimax pure strategy for B is to play column 1.

Value of the game = 45.035.0

5.3 (b) (i) Let As strategy be pp 1 .Bs strategy As expected pay-off

Column 1 41431 pppy Column 2 1615

2 pppy

Column 3 67163 pppy Using graphical method,

At the maximin point,

13

7

6716

p

pp

Hence, the optimal mixed strategy for A is to play row 1 with

probability13

7and row 2 with probability

13

6.

(ii) Value of the game =13

291

13

76

.

B1

M1

A1

M1

A1

D2

M1

A1

M1A1

11 marks

7 (a) Revenue function, 22400 qqr

Profit function, 40042.02400 22 qqqqP 4003962.2

2 qq

(b) 03964.4 qdq

dP

90q

04.42

2

dq

Pd

Hence, profit is maximum when the level of output is 90 units.

(c) At maximum profit, 90q .

Price, 220RM902400 p

B1M1

A1

M1

A1

A1

M1A1

6

5

4

3

2

1

0

1

p1

1y

2y

3y


4/5

STPM950/3 (2013) 4

(d) Maximum profit 40090396902.2 2 17420RM

(e) With a tax of RM22 per unit on the product,

400262.0

2240042.0

2

2

qq

qqqc

400262.02400 22 qqqqP

4003742.2 2 qq

03744.4 qdq

dP

85q

04.42

2

dq

Pd

Profit is maximum when the level of output is 85 units.

New price, 230RM852400 p

M1

A1

B1

B1

M1

M1A115 marks

8. (a)

D1Sequence

D1All arrows

D1All correct

B1at least 5 EST correctB1all EST correct

B1at least 5 LST correct

B1all LST correct

(b) Critical activities are B, D, G, I. B1

Minimum time to complete the project is 21 days. B1

Finish

21 21

A 7

0 4

B 5

0 0

Start

0 0

C 4

7 11

D 7

5 5

E 4

12 15

H 2

16 19

F 6

5 6

G 5

12 12

I 4

17 17

J 3

11 18

Act Dur

EST LST


5/5

STPM950/3 (2013) 5

(c) Minimum project completion time is 22 days. B1

Time (day)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22

B(5) D(4) C(2) E(3) H(3)A(3) F(3) G(5) I(3)

J(2)

8 8 8 8 8 7 7 7 7 7 7 7 5 7 7 7 8 8 8 8 8 6

J

A

F

G I

B D

C E H

Gantt chart:

D1precedence relationship

D1number of workers not more than 8 men/day

D1complete in 22 days

Resource histogram:

D2his values

8

7

6

5

4

3

2

1

0Resourcerequirement(men/day)

seafield selangor 2013 m3(a)

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