August 1997
QT211: QUANTITATIVE ANALYSIS FOR MANAGEMENT

QUESTION 5

Total Marks: 20 Marks

 Click here to access other questions

SUGGESTED SOLUTIONS
Solutions and allocated marks are indicated in green.
Return to Question 5
5. (a) A construction project consists of the activities given in the table above:
(i) Construct the complete network diagram for this project. [8]
A correctly labelled network diagram is shown below. 0.5 marks should be deducted for each error or omission in the diagram, with a minimum mark of 0 marks, and a maximum mark of 8 marks.

[8 marks]
(ii) Using the network diagram, or otherwise, determine the critical path for this project. [2]
Activity Immedeciate Predecessor(s) Duration (in months)
A NONE 8
B NONE 4
C A 4
D A 2
E C, D 3
F B 2
G NONE 1
H E, F 2
I H, G 3
J I 4
K J 3
L K 4
The critical pathis A C E H I J K L with a duration of 31 weeks.
[2 marks]
(b) High Spirits is a distributor of low-cost wines. They have recently introduced into the market a wine called 'Cheap thrill' to improve sales. This wine sells at $5 per bottle. High Spirits' inventory carrying cost is estimated to be 10% per annum, and there is a $20 transportation charge levied when customers place orders.
(i) If the demand is for this new wine is expected to be constant at a rate of 9600 bottles per year, determine the EOQ (economic order quantity) for the wine. [4]
Demand, D = 9600 bottles per year, Carrying Cost, Cc = 10% of $5 = $0.5, and Cost of Ordering, C0 = $20 [1]

[4 marks]
(ii) Based on the EOQ, how many times will High Spirits replenish its stock every year? [2]
Number of orders = D/EOQ = 9600/877 = 11 per year
[2 marks]
(iii) What is the estimated annual total cost associated with 'Cheap Thrill'? [4]
(Include purchasing costs in your calculation).
Total inventory cost/year = Ordering cost/year +
Annual carrying cost +
Annual purchasing cost (1 mark)
= (11 X $20) + [(877/2) X 0.1 X $5]
+ (9600 X $5) (2 marks)
= $220 + $219.25 + $48000
= 48439.25 (1 mark)
[4 marks]