# Question 8:

## Part (a):

| Answer | Marks | Guidance |
|--------|-------|----------|
| $x = 4$ (since D has earliest start 5, duration $x$, and latest finish 9, so $x = 9 - 5 = 4$) | B1 | |
| $z = 17$ (latest finish for G; earliest start 9, duration 8, so earliest finish = 17, hence $z = 17$) | B1 | Accept correct values seen on diagram |
| $y = 19$ (latest finish for H minus duration 5 = 24 - 5 = 19) | (implied) | $x$, $y$, $z$ — two values correct for B1B1 |

**Award: B1 for $x = 4$, B1 for $z = 17$ (and $y = 19$ implied)**

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## Part (b):

| Answer | Marks | Guidance |
|--------|-------|----------|
| B, D, G, I, K | B1 | Must be a path; all activities stated |

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## Part (c)(i):

| Answer | Marks | Guidance |
|--------|-------|----------|
| The critical path is B, D, G, I, K with total length 28 weeks | M1 | Identifying critical path length and need to reduce it |
| G can be reduced by up to 3 weeks (min 5); reduce G by 3 weeks at cost £6000/week | A1 | Justification: G is on critical path; reduction of 3 weeks |
| F is on path A, C, F, J, K (length = 5+3+7+9+4 = 28); reducing G also requires checking this path | M1 | Recognising other paths become critical |
| F must also be reduced by 3 weeks (down to 4, its minimum); cost £7000/week | A1 | Justified by F path also being length 28 |
| E: path through E = 9+6+5+4 = 24; not critical after reductions, so E need not be reduced | A1 | |

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## Part (c)(ii):

| Answer | Marks | Guidance |
|--------|-------|----------|
| Revised minimum completion time = **25 weeks** | B1 ft | Follow through from (c)(i) |

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## Part (c)(iii):

| Answer | Marks | Guidance |
|--------|-------|----------|
| G reduced by 3 weeks: $3 \times £6000 = £18000$ | M1 | |
| F reduced by 3 weeks: $3 \times £7000 = £21000$ | | |
| Total additional cost = $£18000 + £21000 = £\mathbf{39000}$ | A1 | cao |