## Question 6:

### Part (a):

| Answer/Working | Marks | Guidance |
|---|---|---|
| Precedence table: A–; B–; C–; D–A; E–A; F–BE; G–BE; H–C; I–DF; J–CDFG; K–H | B2, 1, 0 **(2)** | |

### Part (b):

| Answer/Working | Marks | Guidance |
|---|---|---|
| Early times correct for first set of nodes | 1M1, 1A1 | |
| All early and late times correct | 2M1, 2A1 **(4)** | |

### Part (c):

| Answer/Working | Marks | Guidance |
|---|---|---|
| Total float on $E = 21 - 5 - 3 = 13$ | M1, A1 **(2)** | |

### Part (d):

| Answer/Working | Marks | Guidance |
|---|---|---|
| $\frac{62}{28} = 2.21$, so lower bound is 3 workers | M1, A1 **(2)** | |

### Part (e):

| Answer/Working | Marks | Guidance |
|---|---|---|
| Correct scheduling diagram on 3 workers up to time 30, e.g. Worker 1: A, E, D, I; Worker 2: B, F, G, J; Worker 3: C, H, K | 1M1, 1A1, 2A1, 3A1 **(4)** | |

# Question 6:

## Part a:
| Answer | Marks | Guidance |
|--------|-------|----------|
| Any 3 rows completed correctly | a1B1 | |
| All five rows completed correctly | a1B2 | |

## Part b:
| Answer | Marks | Guidance |
|--------|-------|----------|
| All top boxes complete, values generally increasing left to right | b1M1 | Condone one rogue |
| CAO | b1A1 | |
| All bottom boxes complete, values generally decreasing R to L | b2M1 | Condone one rogue; condone missing 0 or 28 for M only |
| CAO | b2A1 | |

## Part c:
| Answer | Marks | Guidance |
|--------|-------|----------|
| Correct calculation, all three numbers correct (ft). Float $\geq 0$ | c1M1 | |
| CAO | c1A1 | |

## Part d:
| Answer | Marks | Guidance |
|--------|-------|----------|
| Attempt to find lower bound: $[52\text{-}72 \div \text{their finish time}]$ | d1M1 | Accept awrt 2.2 |
| CAO – correct calculation seen or awrt 2.2 | d1A1 | Beware $28/11$ gives 3 also, so 3 with no working gets M0A0 |

## Part e:
| Answer | Marks | Guidance |
|--------|-------|----------|
| Not a cascade chart; 4 workers used at most; at least 7 activities | e1M1 | If in doubt send to review |
| CHKAB correct: C-14; H-10; K-4; A-5; B-9. A and B completed by late finish times (A by time = 18, B by time = 21) | e1A1 | |
| 3 workers; all 11 activities present (just once); condone one error either precedence or activity length on activities D, E, F, G, I, J | e2A1 | |
| 3 workers; all 11 activities present (just once); no errors on activities D, E, F, G, I, J | e3A1 | |

**Precedence checks:**
- F must not start until after B and E are complete
- G must not start until after B and E are complete
- J must not start until after C, D, F are complete
- I must not start until after D and F are complete

**Length checks:**
- Length 5: A, I
- Length 4: D
- Length 3: E, G, J
- Length 2: F
- Length 9: B

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