D1 June 2010 Q8

EdexcelOld spec11 marksCritical Path Analysis

Figure 7: activity network with activities A (4), B (2), C (3), D (5), E (6), F (9), G (10), H (2), I (4), J (5), K (3), L (6) and four dummies — Figure 7

A project is modelled by the activity network shown in Figure 7. The activities are represented by the arcs. The number in brackets on each arc gives the time, in days, to complete the activity. Each activity requires one worker. The project is to be completed in the shortest possible time.

(a) Complete Diagram 2 in the answer book to show the early and late event times. (4)

(b) State the critical activities. (1)

(d) Use your cascade chart to determine a lower bound for the number of workers needed.
You must justify your answer. (2)

Scheme	Marks
	M1 A1 M1 A1
	(4)

Scheme	Marks
Critical activities: C E H J L	B1
	(1)

Cascade chart: critical C, E, H, J, L along the top from 0 to 22; A 0–4 float to 6; B 0–2 float to 3; D 4–9 float to 11; F 3–12 float to 16; G 3–13 float to 16; I 9–13 float to 16; K 13–16 float to 22 — Mark scheme (c)

Scheme	Marks
	M1 A1 A1 A1
	(4)

Mark scheme (d)

Scheme	Marks
4 workers needed e.g. at time 8 ½ (noon on day 9) activities E, D, F and G must be happening.	B2, 1, 0
	(2)
	(11 marks)

Notes

1B1: A correct statement, details of either time (7<time<9, 8<day<10), or activities, bod gets B1. Allow 1 B mark (only) on ft from their 12 activity, 7 float diagram.

2B1: A correct, complete full statement details of time and activities.