Southern College
Kolej Selatan
南方学院
Final Examination
Semester 1 / Year 2008
COURSE
COURSE CODE
TIME
DEPARTMENT
CLASS
LECTURER
: QUANTITATIVE METHOD AND DATA ANALYSIS
: MATH1123
: 2 1/2 HOURS
: COMPUTER SCIENCE
: IT07-B, IT07-A, IT06-C
: LOW FEE NGOO
Student’s ID
Batch No
:
:
Notes to candidates:
1) The question paper consists of 4 page and 4 questions.
2) Answer all questions.
3) Return the question paper with your answer booklet.
QUANTITATIVE METHOD AND DATA ANALYSIS
1. A publisher is printing a new book. This book may be either a hard cover book or a
paperback. There is a RM4 profit on each hard cover and RM3 profit on each paperback.
It takes 3 minutes to bind a hard covered book and 2 minutes to bind a paperback. The
total available time for binding is 800 hours. Through experience the publisher knows that
he needs at least 10 000 hard covered editions and not more than 6 000 paperbacks. Find
the number of paperbacks and hard covered editions that must be printed in order to obtain
the maximum profit.
(25 marks)
2. (a) The network for a small building project is shown as Figure 1 below, together with
the time, in days, required to complete each task.
F
7
7
A
3
C
2
D
3
7
B
3
4
G
6
END
5
E
Figure 1
You are required to list the possible paths through the network and the length of the
path ( in days) in each case. Then, state the critical path and the project duration.
(10 marks)
(b) Creative Builders have been awarded a contract to build an office block. The project
has been broken down into a number of activities as Table 1 below. The overheads
on this project are RM5000 per month. Construct a network diagram for this project
and hence determine the minimum project duration and its associated cost. (15 marks)
Page 1 of 4
QUANTITATIVE METHOD AND DATA ANALYSIS
Activity
Immediately
Duration in months
Total cost (RM ’000)
preceding activity
A
−
8
100
B
−
2
75
C
A
3
135
D
A
7
70
E
B
5
160
F
C, D
9
255
G
D
2
30
H
D, E
4
90
I
G, H
3
55
Table 1
3. (a) The economic order quantity (EOQ) is one of the oldest and most commonly known
inventory control techniques. It is relatively easy to use, but it does make a number
of assumptions. State five assumptions usually made in EOQ calculation. (10 marks)
(b) ABC Electronics supplies microcomputer circuitry to a company that incorporates
microprocessors into refrigerators and other home appliances. One of the components
has an annual demand of 250 units, and this is constant throughout the year. Carrying
cost is estimated to be $1 per unit per year, and the ordering cost is $20 per order.
(i) How many units should be ordered each time and order is placed to minimize
the cost?
( 4 marks)
(ii) How many orders per year are needed with the optimal policy?
( 3 marks)
(iii) What is the average inventory if costs are minimized?
( 3 marks)
(iv) If the ordering cost is not $20, and ABC Electronics has been ordering 150 units
each time an order is placed. For this order policy to be optimal, what would the
ordering cost have to be?
( 5 marks)
Page 2 of 4
QUANTITATIVE METHOD AND DATA ANALYSIS
4. (a) State five characteristics of a simple queue.
(10 marks)
(b) The Muthu Cobbler heel bar employs 3 operators who can on average each repair the
heels of 5 pairs of shoes an hour. If the average number of customers requiring
service is 12 per hour, calculate
(i)
traffic intensity.
( 3 marks)
(ii) Probability that of there being no units in the system
( 3 marks)
(iii) the average time a customer is in the system.
( 3 marks)
(iv) the average number of customers in the system
( 3 marks)
(v) whether any time would be saved for customers if the three channel system with
a service rate of 5 per hour was replaced by a single channel system ( 3 marks)
000
Page 3 of 4
QUANTITATIVE METHOD AND DATA ANALYSIS
LIST OF FORMULAE
Average inventory level =
EOQ = Q * =
TC =
Q
2
2 DC o
ch
D
Q
C0 + Ch
Q
2
Single channel system
Traffic intensity
Probability that of there being
no units in the system
ρ=
λ
µ
ρ0 = 1 −
Average time in the system
W=
Average number in the system
L=
Multi channel system
ρ=
λ
µ
1
µ −λ
λ
µ −λ
Page 4 of 4
P0 =
λ
cµ
c!(1 − ρ )
⎡ n =c −1 1
n⎤
( ρ c) c + c!(1 − ρ ) ⎢ ∑ (ρ c ) ⎥
⎦
⎣ n =0 n!
W=
( p c) c
1
P0 +
2
µ
c!(1 − ρ ) cµ
L=
ρ ( ρ c) c
P0 + ρ c
c!(1 − ρ ) 2