A2 June 2022 Q5

EdexcelCurrent spec14 marksCritical Path Analysis

5.

Figure 2: activity network with early event times: A(4), B(5) and C(7) leave the start (0); A ends at an event with early time 4, from which D(x) leaves and a dummy runs to the event at 11; C ends at an event with early time 7, from which E(4) and F(x) leave; B and E end at the event with early time 11, from which G(3) and H(5) leave; D and G end at the event with early time 14, from which J(7) leaves and a dummy runs to the event at 16; F and H end at the event with early time 16, from which K(6) leaves; J and K end at the finish (22); the late event time boxes are empty
Figure 2

The network in Figure 2 shows the activities that need to be completed for a project. Each activity is represented by an arc and the duration of the activity, in days, is shown in brackets. The early event times are shown in Figure 2.

(a) Complete Table 1 in the answer book to show the immediately preceding activities for each activity. (2)
ActivityImmediately preceding activityActivityImmediately preceding activity
A F 
B G 
C H 
D J 
E K 

Table 1

It is given that \(4 \lt x \leqslant m\)

(b) State the largest possible integer value of \(m\). (1)
(c)
(i) Complete Diagram 1 in the answer book to show the late event times.
(ii) State the activities that must be critical. (3)

[Diagram 1 in the answer book is a copy of Figure 2.]

(d) Calculate the total float for activity G. (1)

The resource histogram in Figure 3 shows the number of workers required when each activity starts at its earliest possible time. The histogram also shows which activities happen at each time.

Figure 3: resource histogram, number of workers against time: 0 to 4, A (3 workers), B (2) and C (1), total 6; 4 to 5, B (2), C (1) and D (2), total 5; 5 to 7, C (1) and D (2), total 3; 7 to 10, E (2), D (2) and F (1), total 5; 10 to 11, E (2) and F (1), total 3; 11 to 13, G (2), H (2) and F (1), total 5; 13 to 14, G (2) and H (2), total 4; 14 to 16, H (2) and J (1), total 3; 16 to 21, J (1) and K (3), total 4; 21 to 22, K (3), total 3
Figure 3
(e) Complete Table 2 in the answer book to show the number of workers required for each activity of the project. (2)
ActivityNumber of workersActivityNumber of workers
A F 
B G 
C H 
D J 
E K 

Table 2

(f) Draw a Gantt chart on Grid 1 in the answer book to represent the activity network. (5)
Grid 1: blank grid with time from 0 to 22
Grid 1
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