位置17的问题 (Zrox) Zrox plans to manufacture a new copier with the activity times and precedence relationships below. Draw the process flow diagram. [table]
| Time | Immediate Activity | (minutes) | predecessor(s) S | 0.2 | -- T | 0.4 | S U | 0.3 | -- V | 1.3 | T, U
W | 0.1 | -- X | 0.8 | W Y | 0.3 | V, X
Z | 1.2 | Y | |
[/table] (Zrox) The process completion time is ___.2.12.42.73.13.43.74.14.4

Question

位置17的问题 (Zrox) Zrox plans to manufacture a new copier with the activity times and precedence relationships below. Draw the process flow diagram. [table]
| Time | Immediate Activity | (minutes) | predecessor(s) S | 0.2 | -- T | 0.4 | S U | 0.3 | -- V | 1.3 | T, U
W | 0.1 | -- X | 0.8 | W Y | 0.3 | V, X
Z | 1.2 | Y |  | 
[/table] (Zrox) The process completion time is ___.2.12.42.73.13.43.74.14.4

BlackTom AI · Accepted Answer

Critical path method: list each activity with its duration and immediate predecessors, then find all paths to the terminal activity Z and pick the longest (the process completion time).

1) Relevant concepts
- Precedence relationships constrain order of activities.
- The process completion time equals the length of the longest path from start to the terminal activity (critical path).
- Add activity times along each path to compute path lengths.

2) Activities and predecessors (from the table)
- S: 0.2, no predecessor (start)
- T: 0.4, predecessor S
- U: 0.3, no predecessor (start)
- V: 1.3, predecessors T and U
- W: 0.1, no predecessor (start)
- X: 0.8, predecessor W
- Y: 0.3, predecessors V and X
- Z: 1.2, predecessor Y

3) Identify possible complete paths to Z and compute sums (showing intermediate steps)
- Path S → T → V → Y → Z:
  - S = 0.2
  - S + T = 0.2 + 0.4 = 0.6
  - S + T + V = 0.6 + 1.3 = 1.9
  - S + T + V + Y = 1.9 + 0.3 = 2.2
  - S + T + V + Y + Z = 2.2 + 1.2 = 3.4
- Path U → V → Y → Z:
  - U = 0.3
  - U + V = 0.3 + 1.3 = 1.6
  - U + V + Y = 1.6 + 0.3 = 1.9
  - U + V + Y + Z = 1.9 + 1.2 = 3.1
- Path W → X → Y → Z:
  - W = 0.1
  - W + X = 0.1 + 0.8 = 0.9
  - W + X + Y = 0.9 + 0.3 = 1.2
  - W + X + Y + Z = 1.2 + 1.2 = 2.4

4) Why the correct answer is correct
The critical path is the longest of these path durations because all precedence constraints must be satisfied and parallel branches cannot shorten the longest chain. The longest computed path is S–T–V–Y–Z with total time 3.4, so the process completion time is 3.4.

5) Why the other choices are incorrect
- 2.1: no path sums to 2.1.
- 2.4: equals the W–X–Y–Z path, but that is shorter than the critical path (so not the overall completion time).
- 2.7: no path equals 2.7.
- 3.1: equals the U–V–Y–Z path, shorter than 3.4.
- 3.7, 4.1, 4.4: larger than any feasible path sum (no combination of given activities yields these values).

6) Conclusion
The process completion time is 3.4, which matches the provided correct answer.

类似问题

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