D1 June 2016 Q7
7.

The network in Figure 6 shows the activities that need to be undertaken by a company to complete a project. Each activity is represented by an arc and the duration, in days, is shown in brackets. Each activity requires exactly one worker. The early event times and late event times are shown at each vertex.
Given that the total float on activity D is 1 day,
It is decided that the company may use up to 36 days to complete the project.
| Scheme | Marks |
|---|---|
| \(w = 11,\ x = 21,\ y = 17,\ z = 4\) | B3, 2, 1, 0 |
| (3) |
Notes
a1B1: Any two values correct (it must be clear which value corresponds to which letter)
a2B1: Any three values correct
a3B1: All four values correct

| Scheme | Marks |
|---|---|
| M1 | |
| A1 | |
| M1 | |
| A1 | |
| (4) |
Notes
b1M1: At least 10 activities including 6 floats. A scheduling diagram scores M0
b1A1: Critical activities dealt with correctly and five other non-critical activities dealt with correctly
b2M1: Exactly 14 activities (just once) including all 10 floats (on the correct non-critical activities) – this mark is not dependent on the previous A mark
b2A1: CAO
| Scheme | Marks |
|---|---|
| At time 12.5, activities H, D, G, I and J must all be happening so 5 workers | M1 A1 |
| (2) |
Notes
c1M1: A statement with the correct number of workers (5) and the correct activities (H, D, G, I and J) with any mention of time (need not be correct)
c1A1: A correct, complete statement with details of both time (\(12 \lt \text{time} \lt 13\)) and activities. Allow ‘on day 13’ or ‘during day 13’ as equivalent to this time interval but not ‘at day 13’ – note strict inequality for the time, for example, at time 12 is A0. Accept the time interval ‘\(12 \lt \text{time} \lt 13\)’ for this mark or a time that implies a time strictly between \(t = 12\) and \(t = 13\)
e.g.

| Scheme | Marks |
|---|---|
| M1 | |
| A1 | |
| A1 | |
| (3) | |
| (12 marks) |
Notes
d1M1: Not a cascade chart. At most 4 workers used and at least 12 activities placed. The completion time must be no greater than 36
d1A1: 3 workers. All 14 activities present (just once). Condone two errors either precedence or activity duration. The completion time must be no greater than 36 – see table below for IPA and duration for each activity. One activity can give rise to at most two errors; one on duration and one on IPA
d2A1: 3 workers. All 14 activities present (just once). No errors. The completion time must be 36
| Activity | Duration | IPA |
|---|---|---|
| A | 5 | - |
| B | 7 | - |
| C | 3 | - |
| D | 11 | A |
| E | 4 | A |
| F | 5 | C |
| G | 7 | B, E, F |
| H | 8 | B, E, F |
| I | 12 | B, E, F |
| J | 10 | C |
| K | 13 | D, G, H |
| L | 5 | D, G, H |
| M | 6 | H |
| N | 8 | I, J |