**Part (a)**

| Activity | Immediately preceded by | Activity | Immediately preceded by | Activity | Immediately preceded by |
|----------|------------------------|----------|------------------------|----------|------------------------|
| A | - | G | A, B, E | M | D, G |
| B | - | H | A, B, E | N | H, K |
| C | - | I | A, B, E | P | H, K |
| D | A | J | A, B, E, F | Q | H, I, J, K |
| E | C | K | D, G | R | P, Q |
| F | C | L | D, G | | |

| | B2, 1, 0 | (2) |

**Part (b)**

| All top boxes complete, values generally increasing in the direction of the arrows | M1 |  |
| | A1 | (4) |
| All bottom boxes complete (but condone a blank box for the late event time at the end event node for the M mark only). Values generally decreasing in the opposite direction of the arrows | M1 |  |
| | A1 |  |

**Part (c)**

| Critical activities: C, E, G, K and N | B1 | (1) |

**Part (d)**

| Float on J = 35 – 22 – 5 = 8 | B1 ft | (1) |

**Part (e)**

| Lower bound is $\frac{133}{43} = 3.0930... = 4$ | B1 | (1) |

**Part (f)**

| Gantt chart showing: | M1 | (4) |
| - 4 workers | A1 |  |
| - All 14 new (17 in total) activities present (just once) | A1 |  |
| - No errors (or at most three errors). An activity can give rise to at most three errors: one on duration, one on time interval and only one on IPA | A1 |  |

| | | (13 marks) |

**Notes for Question 4:**

**a1B1:** Any four (of the eight blank) rows correct

**a2B1:** All eight rows correct

**b1M1:** All top boxes complete, values generally increasing in the direction of the arrows (so generally going from 'left to right' across the network). Condone one 'rogue' value (if values do not increase in the direction of the arrows then if one value is ignored and the remaining values do increase in the direction of the arrows then this is considered to be a single rogue value). Note that all values in the top boxes could be incorrect but it can still score the M mark if the values are **increasing in the way stated above**

**b1A1:** CAO – all values correct in the top boxes

**b2M1:** All bottom boxes complete (but condone a blank box for the late event time at the end event node for the M mark only). Values generally decreasing in the opposite direction of the arrows (so generally going from 'right to left' across the network). Condone one 'rogue' (as described above in b1M1)

**b2A1:** CAO – all values correct in the bottom boxes

**c1B1:** CAO (C, E, G, K and N only)

**d1B1ft:** correct calculation seen for their J (provided total float is non-negative). Correct answer or the correct answer following through the event times for J with no working seen scores B0 – must see all three numbers in their calculation

**e1B1:** CSO – 4 together with **either a correct calculation seen or an awrt 3.1**. An answer of 4 with no working scores B0. If working seen then it must be correct

**f1M1:** Not a cascade (Gantt) chart. 5 'workers' used at most and at least 8 new (11 in total) activities placed. Condone at most **three errors**. An activity can give rise to at most three errors: one on duration, one on time interval and only one on IPA

**f1A1:** 4 workers. All 14 new (17 in total) activities present (just once). Condone at most **three errors**. An activity can give rise to at most three errors: one on duration, one on time interval and only one on IPA

**f2A1:** 4 workers. All 14 new (17 in total) activities present (just once). Condone **one error either on precedence or time interval or activity length**; An activity can give rise to at most three errors: one on duration, one on time interval and only one on IPA

**f3A1:** 4 workers. All 14 new (17 in total) activities present (just once). No errors.

**The table below is helpful in checking an activities duration, time interval and IPA**

| Activity | Duration | Time interval | IPA |
|----------|----------|----------------|-----|
| D | 12 | 9 – 23 | A |
| E | 3 | 9 – 12 | C |
| F | 13 | 9 – 30 | C |
| G | 11 | 12 – 23 | A, B, E |
| H | 8 | 12 – 30 | A, B, E |
| I | 12 | 12 – 35 | A, B, E |
| J | 5 | 22 – 35 | A, B, E, F |
| K | 7 | 23 – 30 | D, G |
| L | 6 | 23 – 43 | D, G |
| M | 6 | 23 – 43 | D, G |
| N | 13 | 30 – 43 | H, K |
| P | 7 | 30 – 40 | H, K |
| Q | 5 | 30 – 40 | H, I, J, K |
| R | 3 | 37 – 43 | P, Q |

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