Identify critical path and activities

4 Henry is planning a surprise party for Lucinda. He has left the arrangements until the last moment, so he will hold the party at their home. The table below lists the activities involved, the expected durations, the immediate predecessors and the number of people needed for each activity. Henry has some friends who will help him, so more than one activity can be done at a time.

1. Draw an activity network to represent these activities and the precedences. Carry out forward and reverse passes to determine the minimum completion time and the critical activities. If Lucinda is expected home at 7.00 p.m., what is the latest time that Henry or his friends can begin telephoning the other friends?
2. Draw a resource histogram showing time on the horizontal axis and number of people needed on the vertical axis, assuming that each activity starts at its earliest possible start time. What is the maximum number of people needed at any one time?
3. Now suppose that Henry's friends can start buying the food and making the decorations as soon as the telephoning begins. Construct a timetable, with a column for 'time' and a column for each person, showing who should do which activity when, in order than the party can be organised in the minimum time using a total of only six people (Henry and five friends). When should the telephoning begin with this schedule?

1 [Figure 1, printed on the insert, is provided for use in this question.]
A building project is to be undertaken. The table shows the activities involved.

1. Complete an activity network for the project on Figure 1.
2. Find the earliest start time for each activity.
3. Find the latest finish time for each activity.
4. State the minimum completion time for the building project and identify the critical paths.

1 Which of the following statements about critical path analysis is always true? Tick ( \(\checkmark\) ) one box. All activity networks have exactly one critical path. □ All critical activities have a non-zero float. □ The first activity in a critical path has an earliest start time of zero. □ A delay on a critical activity may not delay the project. □

Activity	Time	Precedence
A	5
B	20	A
C	3	A
D	7	A
E	4	B
F	15	C
G	6	C
H	17	D
I	10	F, G
J	2	G, H
K	6	E, I
L	9	I, J
M	3	K, L

Fig. 1 Construct an activity network Use appropriate forward and backward scanning to find

1. the minimum number of days needed to complete the entire project, [3 marks]
2. the activities which lie on the critical path. [3 marks]

[6 marks]