位置2的问题 (Small Project) [table]
| Immediate | Activity Activity | predecessor(s) | time (days) W | --- | 4 X | --- | 5 Y | W, X | 6
Z | W, X | 7
| |
[/table] (Small Project) The latest start time (LST) of Z is ___.56789

Question

位置2的问题 (Small Project) [table]
| Immediate | Activity Activity | predecessor(s) | time (days) W | --- | 4 X | --- | 5 Y | W, X | 6
Z | W, X | 7
| | 
[/table] (Small Project) The latest start time (LST) of Z is ___.56789

BlackTom AI · Accepted Answer

Backward pass in CPM: LST = LF − duration. Determine ES/EF forward, find project completion, then do backward pass.

Forward pass (compute earliest starts/finishes):
- W: ES_W = 0 (no predecessors). EF_W = ES_W + dur_W = 0 + 4 = 4.
- X: ES_X = 0 (no predecessors). EF_X = 0 + 5 = 5.
- Y (predecessors W and X): ES_Y = max(EF_W, EF_X) = max(4,5) = 5. EF_Y = 5 + 6 = 11.
- Z (predecessors W and X): ES_Z = max(EF_W, EF_X) = max(4,5) = 5. EF_Z = 5 + 7 = 12.

Project completion time = max(EF of terminal activities) = max(EF_Y, EF_Z) = max(11,12) = 12 days.

Backward pass (compute latest finishes/starts):
- For terminal activities, LF = project completion time = 12.
  - LF_Z = 12 ⇒ LST_Z = LF_Z − dur_Z = 12 − 7 = 5.
  - LF_Y = 12 ⇒ LST_Y = 12 − 6 = 6.
- For predecessors:
  - W has successors Y and Z with LSTs 6 and 5; LF_W = min(6,5) = 5 ⇒ LST_W = 5 − 4 = 1.
  - X has successors with LSTs 6 and 5; LF_X = min(6,5) = 5 ⇒ LST_X = 5 − 5 = 0.

Why the correct answer is 5:
- Z’s LF is the project finish time (12). Subtracting its duration (7) yields LST_Z = 12 − 7 = 5. Z’s earliest start ES_Z is also 5, so Z has zero slack and is on the critical path.

Why other options are incorrect:
- 6, 7, 8, 9 do not match the backward-pass calculation. For example, 6 would imply LF_Z = 13 (6 + 7) which exceeds the project finish time 12, impossible under backward pass. 7, 8, 9 similarly contradict the computed project finish and EF_Z.

Conclusion: The latest start time (LST) of Z is 5, which matches the provided correct answer.

位置2的问题 (Small Project) [table] | Immediate | Activity Activity | predecessor(s) | time (days) W | --- | 4 X | --- | 5 Y | W, X | 6 Z | W, X | 7 | | [/table] (Small Project) The latest start time (LST) of Z is ___.56789单项选择题

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