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# Critical Path and Slack Time

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1. Which of the following is a critical path from milestone A to milestone K?

2. What is the slack time for the activity starting at milestone F?

3. What is the length of the critical path identified in question 1?

4. Which milestones are precursors to J?

Please see attachment for complete question.

https://brainmass.com/computer-science/algorithms/critical-path-slack-time-487405

#### Solution Preview

Please find the explanations (in layman terms) along with the answers below.

Critical path from milestone A to milestone K is the path that ensures that all the intermediate activities are completed, and in minimum time.

Since there are two parallel paths between milestone A and milestone H, and similarly two parallel paths between milestones H and milestone K, we can break the original requirement into two sub-parts:
- finding critical path from milestone A to milestone H, and
- finding critical path from milestone H to milestone K.

Finding critical path from milestone A to milestone H:

Path ABDFH: length = 7 + 2 + 6 + 2 = 17
Path ACEGH: length = 5 + 3 + 10 + 4 = 22

Since all the milstones (A,B,C,D,E,F,G) and activities (represented by edges in the graph) along different parallel paths must be achieved/completed before arriving at milestone H, this can not happen until time 22.

Critical path from milestone A to milestone F is ABDF (only path from A to F) with ...

#### Solution Summary

Solution gives detailed layman explanations and computations that should help you understand how the answers are arrived at. After going through it you can easily choose the correct multiple-choice-option in each of the given questions.

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## Calculating critical paths and slack time

2) Cosider the network pictured below with task durations in days as follows:
A=2, B= 6, C=5, D=2, E=6, and F=1

a) Enumerate all paths and their duration through this network
b) Calculate the critical path for the network
c) What is the minimum duration of the project?
d) How much slack exists at each activity

A----------C----------E
Start End
B-----------D----------F

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