BACHELOR OF BUSINESS ADMINISTRATION WITH HONOURS

SEMESTER JAN 2014BBMP1103 MATHEMATICS FOR MANAGEMENT MATRICULATION NO:791016145081001IDENTITY CARD NO.: 791016-14-5081TELEPHONE NO.: 019-6641264E-MAIL : arman_saad@yahoo.comLEARNING CENTRE: SHAH ALAMTABLE OF CONTENTS

PAGEQUESTION NO. 1

3 5

QUESTION NO . 2

6 7

QUESTION NO . 3

8 9

QUESTION NO . 4

10- 11

Question 1x + 2y + z = 4

3x + z = 2

X y + z = 1

a) Function into a matrix form, let A be the coefficient matrix

1 2 1

x

4

3 0 1y

2

1 -1 1z

1

A = 1 2 1

3 0 1

1 -1 1

b) Determinant of A = 1 0 1 -2 3 1 + 1 3 0 -1 1 1 1 1 -1

= 1 (1) -2 (2) + 1 (3)

= 1 - 4 + (-3)

= -6

c) Minor of A = 1 2 -3

3 0 -3

2 -2 -6d) Cofactor of A = 1 x 1 = 1-1 x 3 = -31 x 2 = 2 -1 x 2 = -21 x 0 = 0-1 x (-2) = 2

1 x 3 = 3 -1 x (-3) = 31 x (-6) = -6

= 1 -2 -3

-3 0 3

2 2 -6e) Adjoint of A = ( Cofactor A )

= 1 -2 -3

-3 0 3

2 2 -6

= 1 -3 2

-2 0 2

-3 3 -6

f) Inverse of A

A-1 = 1/-6 X 1 -3 2

-2 0 2

-3 3 -6

= 1/6 -3/6 2/6

-2/6 0 2/6

-3/6 3/6 -6/-6

g) x , y and zx

1/-6-3/-62/-6

4

2

y= -2/-6 02/-6

2=0

z

-3/-63/-6-6/-6

1

3

Thus, x = 2 , y = 0 and z = 3Question 2

a) 3x + 10y 4 = 03x + 10y = 4

10y = -3x + 4

Y = -3/10 x + 4/10

M = 10/3

Y = mx + b through point ( 1,4)

4 = 10/3 (1) + b

4 = 10/3 + b

B = 4/1 10/3

= 12 10 3 = 2/3

Therefore, y = 10/3 x + 2/3

b) Y = x2 12x + 14 = 0Y = x2 12x = -14

a = 1Y = x2 12x +36 = -14 + 36

b = -12

Y = ( x b/2)2 = 22

c = 14

Y = ( x 12/2)2 = 22Y = (x 6)2 = 22

Y = ( x 6 )2 = 22Y = x 6 = +- 22X = 6 +- 22

Therefore x = 6 22 and -6 22Question 3a) Advantages of performing break even analysis

Break even analysis enables a business organization to

Measure profit and losses at different levels of production and sales

To predict the effect of changes price of sales

To analysis the relationship between fixed cost and variable cost To predict the effect on profitability if changes in cost and efficiency.b) I) Break Even Point : Total Revenue = Total Cost

Total revenue = unit price x total quantity sold

= 40q

Total Cost = Variable Cost + Fixed Cost

= 22q + 77,000

Therefore 40q = 22q + 77,000

40q 22q = 77,000

18q = 77,000

Q = 77,000 / 18

Q = 4278

Hence 4278 units have to be sold to reach the break even point.

ii) Profit = Total Revenue Total Cost

Total Revenue = unit price x total quantity sold

= 40q

Total Cost = Variable Cost + Fixed Cost

= 22q + 77,000

Profit = Total Revenue - Total Cost

11,000= 40q - (22q + 77,000)

11,000= 40q 22q 77,000

11,000 + 77,000 = 18q

88,000 = 18q

Q = 88,000 / 18

Q = 4889 units

Therefore units to reach profit RM 11,000 is at 4889 units.

Question 4

Option 1 :

FV = RM 100,000.00

I = 8%

N = 10

PV = FV (1 + i)-n = 100,000 ( 1+ 0.08) -10

= 100,000 ( 1.08) -10

= 100,000

(1.08)10

= 100,000 2.158925

= 46, 319.35

Option 2

Payment for 1st year

PV = 10,000

I = 8%

N = 9

FV = PV (1 +i) n

= 10,000 (1.08)9

= 10,000 (1.999)

= RM 19,999.00

Payment for 5th year

PV = 30,000

I = 8%

N = 5

FV = PV ( 1 + i)n

= 30,000 (1.08)5

= 30,000 ( 1.469328) = RM 44,079.84Total for option 2 = RM 19,999.00 + RM 44,079.84 + RM 40,000

= RM 104, 078.84

Therefore choose option 2 since amount more than RM 100,000.00.BBMP1103