A2 June 2025 Q6

EdexcelCurrent spec13 marksCritical Path Analysis

Figure 3: activity network with activities A(2), B(4), C(3), D(7), E(4), F(5), G(5), H(6), I(10), J(2), K(6), L(10), M(7) and three dummies — Figure 3

A project is modelled by the activity network shown in Figure 3. The activities are represented by the arcs. The number in brackets on each arc gives the time, in hours, to complete the corresponding activity. The project is to be completed in the shortest possible time.

(a) Complete Table 1 in the answer book to show the immediately preceding activities for each activity. (2)

Activity	Immediately preceding activities	Activity	Immediately preceding activities
A		G
B		H
C		I
D		J
E		K
F		L
		M

Table 1

(b) Complete Diagram 1 in the answer book to show the early event times and the late event times. (4)

Diagram 1: the network of Figure 3 with an empty box at each event for the early event time (top) and late event time (bottom) — Diagram 1

Grid 1: blank grid with a time axis from 0 to 24 — Grid 1

Figure 4: resource histogram, number of workers against time in hours: 4 from 0 to 2, 5 from 2 to 3, 8 from 3 to 4, 6 from 4 to 7, 8 from 7 to 8, 9 from 8 to 9, 7 from 9 to 12, 6 from 12 to 13, 5 from 13 to 15, 4 from 15 to 17, 2 from 17 to 20 — Figure 4

The resource histogram in Figure 4 shows the number of workers required when each activity starts at its earliest possible time. When an activity is started it must be completed without interruption. Each activity requires at least one worker.

(d) By considering which activities are happening each hour, and by working backwards from the minimum project completion time, complete Table 2 in the answer book to show the number of workers needed for each activity. (3)

Activity	Number of Workers	Activity	Number of Workers
A		G
B		H
C		I
D		J
E		K
F		L
		M

Table 2

Mark scheme (a)

Scheme

Marks

Activity	IPA	Activity	IPA
A	-	G	A, B, E
B	-	H	D, G
C	-	I	A, B, E
D	A	J	H, I
E	C	K	A, B, E
F	C	L	A, B, E, F
		M	A, B, E, F

B1
B1

1.1b
1.1b

(2)

Notes

a1B1: Five correct rows (not including A, B and C)

a2B1: All rows correct (accept blanks for A, B and C)

activity network with early and late event times: start 0, 0; end of A 2, 5; end of C 3, 3; node after B and E 7, 7; end of D and G 12, 12; end of H and I 18, 18; end of F 8, 10; end of J and K and L 20, 20; finish 20, 20 — Mark scheme (b)

Gantt chart: critical activities C 0-3, E 3-7, G 7-12, H 12-18, J 18-20 on the top row; A 0-2 float to 5, B 0-4 float to 7, D 2-9 float to 12, F 3-8 float to 10, I 7-17 float to 18, K 7-13 float to 20, L 8-18 float to 20, M 8-15 float to 20 — Mark scheme (c)

Scheme	Marks	AO
	M1 A1 M1 A1	1.1b 1.1b 1.1b 1.1b
	(4)

Scheme	Marks	AO
	M1 A1 A1 A1	2.1 1.1b 1.1b 1.1b
	(4)

Activity	Start	Late End	Float	Critical	Start	End
A	0	5	3	C	0	3
B	0	7	3	E	3	7
D	2	12	3	G	7	12
F	3	10	2	H	12	18
I	7	18	1	J	18	20
K	7	20	7
L	8	20	2
M	8	20	5