位置12的问题 (Office Move) Consider the following activities: [table]
Activity | Description | Immediate predecessor(s) | Activity time (days) T | Find a location | --- | 8 U | Order furniture | T | 6 V | Interview | --- | 4 W | Hire and train | V | 9 X | Remodel | T | 11 Y | Setup furniture | U | 3 Z | Move in | W, X, Y | 1
| | |
[/table] Draw the project network. (Office Move) The latest start time (LST) of activity X is ___.0681016171819

Question

位置12的问题 (Office Move) Consider the following activities: [table]
Activity | Description | Immediate predecessor(s) | Activity time (days) T | Find a location | --- | 8 U | Order furniture | T | 6 V | Interview | --- | 4 W | Hire and train | V | 9 X | Remodel | T | 11 Y | Setup furniture | U | 3 Z | Move in | W, X, Y | 1
| |  | 
[/table] Draw the project network. (Office Move) The latest start time (LST) of activity X is ___.0681016171819

BlackTom AI · Accepted Answer

Critical-path (CPM) logic and forward/backward passes give latest start times. Use these activity labels and data (as implied by the table): 
T = Find a location, dur = 8, preds = none
U = Order furniture, dur = 6, preds = T
V = Interview, dur = 4, preds = none
W = Hire & train, dur = 9, preds = V
X = Remodel, dur = 11, preds = T
Y = Setup furniture, dur = 3, preds = U
Z = Move in, dur = 1, preds = W, X, Y

1) Forward pass (compute earliest start ES and earliest finish EF):
- T: ES = 0, EF = 0 + 8 = 8
- U: ES = EF(T) = 8, EF = 8 + 6 = 14
- V: ES = 0, EF = 0 + 4 = 4
- W: ES = EF(V) = 4, EF = 4 + 9 = 13
- X: ES = EF(T) = 8, EF = 8 + 11 = 19
- Y: ES = EF(U) = 14, EF = 14 + 3 = 17
- Z: ES = max(EF(W), EF(X), EF(Y)) = max(13, 19, 17) = 19, EF = 19 + 1 = 20

Project completion time = 20 days.

2) Backward pass (compute latest finish LF and latest start LS), start from project end LF(Z) = 20, so LS(Z) = 19:
- For predecessors of Z:
  - W: LF(W) = LS(Z) = 19 => LS(W) = 19 − 9 = 10
  - X: LF(X) = LS(Z) = 19 => LS(X) = 19 − 11 = 8
  - Y: LF(Y) = LS(Z) = 19 => LS(Y) = 19 − 3 = 16
- U is a predecessor of Y (and only constrained by successors): LF(U) = LS(Y) = 16 => LS(U) = 16 − 6 = 10
- T is a predecessor of U and X so LF(T) = min(LS(U), LS(X)) = min(10, 8) = 8 => LS(T) = 8 − 8 = 0
- V: LF(V) = LS(W) = 10 => LS(V) = 10 − 4 = 6

3) Conclusion and interpretation:
Latest start time for activity X (LS(X)) = 8 days. That equals its earliest start (ES = 8) so X lies on a critical path (no slack).

Why other choices are wrong (brief):
- 0, 6, 10, 16, 17, 18, 19 do not match the backward-pass computation for LS(X) = LF(X) − dur(X) = 19 − 11 = 8. For example LS = 14 (not in options) would come from a different predecessor structure; LS = 0 or 6 would violate the required LF(X)=19 determined by the finish constraint of the final activity Z.

Therefore the correct latest start time for X is 8, which matches the provided answer.

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