A2 October 2021 Q2

EdexcelCurrent spec9 marksCritical Path Analysis

Figure 2: activity network: A(4), B(6) and C(10) leave the start; D(2) and E(4) follow A; B and E end at the same event, from which a dummy runs up to the end of D, and H(7), I(2) and F(5) leave; G(6) follows the end of D and the dummy; C and F end at the same event, from which a dummy runs to the end of I, and L(7) and M(5) leave; J(7) follows G and H; K(6) follows the end of I and the dummy; J, K and L end at the finish; a dummy runs from the end of M to the finish — Figure 2

A project is modelled by the activity network shown in Figure 2. The activities are represented by the arcs. The number in brackets on each arc gives the time, in hours, to complete the corresponding activity.

(a) 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 2 with an empty box at each event for the early event time (top) and late event time (bottom) — Diagram 1

Each activity requires one worker and the project must be completed in the shortest possible time using as few workers as possible.

(b) Calculate a lower bound for the number of workers needed to complete the project in the shortest possible time. You must show your working. (2)

Grid 1: blank scheduling grid with time from 0 to 26 — Grid 1

Diagram 1 completed (early, late): start 0, 0; end of A 4, 4; end of D 8, 9; end of B and E 8, 8; end of G and H 15, 15; end of I 13, 16; end of C and F 13, 15; end of M 18, 22; finish 22, 22 — Mark scheme (a)

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

Mark scheme (b)

Scheme	Marks	AO
\(\dfrac{71}{22} = \ldots\)	M1	1.1b
…= 3.22… therefore 4 workers	A1	2.2a
	(2)

Notes

(b) M1: Attempt to find the lower bound (71 \(\pm\) 10) / their completion time (a value of 3.2… seen with no working can imply this mark)

A1: cso - correct calculation seen or 3.2 followed by 4. An answer of 4 with no working scores M0A0

schedule on 4 workers: worker 1 A 0–4, E 4–8, H 8–15, J 15–22; worker 2 B 0–6, D 6–8, G 8–14, I 14–16, K 16–22; worker 3 C 0–10, F 10–15, L 15–22; worker 4 M 15–20 — Mark scheme (c)

Activity	Duration	Time Interval	IPA
A	4	0 – 4	-
B	6	0 – 8	-
C	10	0 – 15	-
D	2	4 – 9	A
E	4	4 – 8	A
F	5	8 – 15	B, E
G	6	8 – 15	B, D, E
H	7	8 – 15	B, E
I	2	8 – 16	B, E
J	7	15 – 22	G, H
K	6	13 – 22	C, F, I
L	7	13 – 22	C, F
M	5	13 – 22	C, F