A2 June 2023 Q2

EdexcelCurrent spec7 marksCritical Path Analysis

Figure 3: activity network: A(3) and C(4) and D(7) leave the start; B(5) follows A; C ends at the same event as B; a dummy runs from the end of D to the end of B and C; E(1) and F(2) leave that event; H(1) follows E; G(4) follows D; F, G and H end at the finish — Figure 3

The network in Figure 3 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)

(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 of the project. (3)

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

The table below lists the number of workers required for each activity in the project.

Activity	Number of workers
A	2
B	1
C	2
D	2
E	3
F	2
G	1
H	3

Each worker is able to do any of the activities. Once an activity is started it must be completed without interruption. It is given that each activity begins at its earliest possible start time.

(b)

(i) On Grid 1 in the answer book, draw a resource histogram to show the number of workers required at each time.

(ii) Hence state the time interval(s) when six workers are required. (4)

Grid 1: blank grid, number of workers from 0 to 8 against time in hours from 0 to 14 — Grid 1

Diagram 1 completed: start 0, 0; end of A 3, 4; end of D 7, 7; end of B and C 8, 9; end of E 9, 10; finish 11, 11 — Mark scheme (a)

resource histogram: 6 workers from 0 to 3, 5 from 3 to 4, 3 from 4 to 7, 2 from 7 to 8, 6 from 8 to 10, 1 from 10 to 11 — Mark scheme (b)

Scheme	Marks	AO
(i)	M1 A1	1.1b 1.1b
(ii) 11 (hours)	A1ft	2.2a
	(3)

Scheme	Marks	AO
(i)	M1 A1 A1	1.1b 1.1b 1.1b
(ii) Six workers are required in the time intervals 0 – 3 and 8 – 10	A1	2.2a
	(4)
	(7 marks)

A2 June 2023 Q2

A2 June 2023 Q2

Notes

Notes