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SCHOOL OF ACCOUNTING &

FINANCE

FM 101 FINANCIAL MATHEMATICS

(F2F Mode)

TEST ONE Marking Guide – SEMESTER 1, 2012

Time allowed: 1 ½ hours plus 5 minutes reading

50 marks (15% of final grade)

INSTRUCTIONS

1.

2.

3.

4.

5.

This test has five (5) questions. ALL questions are compulsory. Write your answers in the ANSWER BOOKLET provided.

This exam paper has a cover page + 3 pages of questions.

You can use silent, non – programmable calculators.

This test is worth 15% of your overall mark.

Question 1

A.

R (x)= 1.79 x

i.

ii.

C (x)= 0.53x + 1071

iii.

Solving R (x)= C (x) for x yields:

1.79 x = 0.53 x + 1071

Þ 1.26 x = 1071

\ x = 850

So, the break-even point is (850,1521.50).

B.

Let x denote the “amount of money invested into AA bonds” and y denote the “amount of money invested into Savings and Loan Certificates”. Then, x+

y = 150000 (1)

0.10 x +

0.05 y =

10000 (2)

Solving equations (1) and (2) simultaneously will yield x = 50000 and y = 100000 . Thus, Mr. Khan should invest $50,000 in AA bonds and $100,000 in Savings and Loan Certificates.

C.

Let x denote the “cost of a medium popcorn” and y denote the “cost of a large coke”. Then,

()

()

Solving equations (1) and (2) simultaneously yields x = 4.50 and y = 2.75. So, a medium popcorn costs $4.50 and a large coke costs $2.75.

Question 2

a. Let x denote “tonnes of Type I steel”, y denote “tonnes of Type II steel”, and

P (x, y ) denote the “profit function”. Thus, the LPP is P (x, y)= 240 x + 80 y

ì 2x +

5 y £ 40,

ï

ï

ï

ï 4x +

y £ 20,

ï

í

ï 10 x +

5 y £ 60,

ï

ï

ï

x, y ³

0.

ï

î

Maximize

subject to

y

20

4x

y

20

12

8

A

B

2x

10 x

0

5

5y

5y

40

60

6

Feasible Region

Coordinates of A :

Solve 2 x + 5 y = 40 and 10 x...

(1)