Quantitative Methods
Foundation Examination
6
September 2011
Autumn 2011
100 marks
–
3 hours
Module A
Additional r
eading time
–
15 minutes
(A
ll questions are compulsory
)
Q.1
(a)
During
annual clearance sale
,
Independent Departmental Store (IDS) reduce
d
the prices of
a product Z by 20%. 40% of the sale of Z was made during the clearance sale and the profit
earned thereon was 25% of cost. Find the profit percentage (on cost) which IDS earned on
product Z during the whole year. (05 marks)
(b)
T
he cost of production of a product
in rupees
is
:
C = 15
x
+ 9,750
where
x
is the number of
items produced. If selling price of each item is Rs. 30, find the sales quantity at which there
would be no profit or loss. (03 marks)
(c)
Find the value of
x
if,
ln
3
+
2
lnx = ln
(
x +
2)
(04 marks)
Q.2
(a)
Bashir has chosen to receive a
pocket money of Rs. 1,200 per week. He was also offered an
alternative by which he would have received Re. 1 on the first day of the week, Rs. 3 on the
second day, Rs. 9 on the third day and so on. Has he taken a wise decision? (04 marks)
(b)
Shiraz borrowed Rs. 120,000 for eight months at 15% simple interest. Compute the
annual
rate of interest, compounded monthly, which would result in the payment of the same
amount of interest. (05 marks)
Q.3 (a) If
1
+
=
u
u
y
and ,15
2
−= xu find dxdy / at x = 2 (05 marks)
(b)
The cost of manufacturing
x
units of a product consists of the following:
Labour
Rs. 0.03
x
2
;
Material
Rs. 220
x;
Overheads
Rs. 50,000
The demand function of the same product
is D(
x
) = 500
–
0.04
x
Required:
(i)
Revenue function and the marginal revenue function.
(ii)
Profit function and the quantity at which profit is
maximised
.
(iii)
Unit price corresponding to maximum profit.
(08 marks)
Q.4
A company has two plants, P
1
and P
2
in two different cities. Each plant manufactures two
products x and y. Daily production of P1 is 50 units of x and 30 units of y. P2 produces 20 units of x
and 15 units of y per day. Each unit of x requires 40 hours of operational, 10 hours of technical
and 5 hours of managerial staff. While each unit of y requires 50 hours of operational, 12 hours of
technical and 7 hours of managerial staff.
Required:
(a)
Construct a mat
rix P depicting the relationship between plants and products and a matrix S
depicting the relationship between products and various categories of staff as described
above. (02 marks)
(b)
(i)
Using the matrices constructed in part (a), compute the matrix R = PS.
(ii)
Based on matrix R, determine the number of total hours worked by each category of
staff, at each plant. (08 marks)
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