D1 June 2006 Q5

EdexcelOld spec15 marksCritical Path Analysis

Figure 4: activity network with events 1 to 9 and activities A(10) to N(12) — Figure 4

An engineering project is modelled by the activity network shown in Figure 4. 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 time.

(a) Calculate the early time and late time for each event. Write these in boxes in Diagram 1 in the answer book. (4)

(b) State the critical activities. (1)

(d) On the grid in the answer book, draw a cascade (Gantt) chart for this project. (4)

The chief engineer visits the project on day 15 and day 25 to check the progress of the work.

Given that the project is on schedule,

(e) which activities must be happening on each of these two days? (3)

Scheme	Marks
	M1 A1 (2) M1 A1 (2)
	(4)

Scheme	Marks
\(A - C - G - I - M\) \(\phantom{A - C -{}} H - K\)	A1
	(1)

Mark scheme (c)

Scheme	Marks
Float on \(D = 21 - 5 - 14 = 2\)	B1ft
Float on \(F = 42 - 20 - 14 = 8\)	M1 A1ft
	(3)

Notes

B1ft cao ft from diagram

M1 method correct or ft correct answer (top ≤ bottom at both ends; must see appropriate working for M1)

A1ft cao ft from diagram

Cascade chart from 0 to 56 days with the critical activities A, C, G, I, M and H, K at the top and floats shaded — Mark scheme (d)

Scheme	Marks
Day 15: \(C\)	B1
Day 25: \(G, H, E, F\)	B2,1,0
	(3)
	(15 marks)