Fm 101 Solution

The University of the South Pacific
Serving the Cook Islands, Fiji, Kiribati, Marshall Islands, Nauru, Niue, Samoa, Solomon Islands, Tokelau, Tonga, Tuvalu, and Vanuatu.

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...