A2 October 2020 Q2

EdexcelCurrent spec15 marksCritical Path Analysis

2.

Figure 1: activity network: A(6), B(7) and C(5) leave the start; D(4) and E(5) follow A; F(3) and G(4) follow B; a dummy from the end of B to the end of C; H(3) follows that event; I(4) runs from the end of E and F up to the end of D; K(5) and L(6) follow; J(6) follows G and H; a dummy from the end of K to the finish; L and J end at the finish
Figure 1

The network in Figure 1 shows the activities that need to be undertaken to complete a project. Each activity is represented by an arc and the duration, in hours, of the corresponding activity is shown in brackets.

(a) Explain why each of the dummy activities is required. (2)
(b) Complete the table in the answer book to show the immediately preceding activities for each activity. (2)
ActivityImmediately preceding activities
A 
B 
C 
D 
E 
F 
G 
H 
I 
J 
K 
L 
(c)
(i) Complete Diagram 1 in the answer book to show the early event times and the late event times.
(ii) State the minimum completion time for the project.
(iii) State the critical activities. (6)
Diagram 1: the network of Figure 1 with an empty box at each event for the early event time (top) and late event time (bottom)
Diagram 1

Each activity requires one worker. Each worker is able to do any of the activities. Once an activity is started it must be completed without interruption.

(d) On Grid 1 in the answer book, draw a resource histogram to show the number of workers required at each time when each activity begins at its earliest possible start time. (3)
Grid 1: blank grid, number of workers from 0 to 6 against time in hours from 0 to 23
Grid 1
(e) Determine whether or not the project can be completed in the minimum possible time using fewer workers than the number indicated by the resource histogram in (d). You must justify your answer with reference to the resource histogram and the completed Diagram 1. (2)
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