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A software project has four phases P1, P2, P3 and P4. Of these phases, P1 Is the first one and needs to be completed before any other phase can commence. Phases P2 and P3 can be executed in parallel. Phase P4 cannot commence until both P2 and P3 are completed. The optimistic, most likely, and pessimistic estimates of the phase completion times in days, for Pl, P2, P3 and P4 are, respectively, (11, 15, 25), (7, 8, 15), (8, 9, 22), and (3, 8, 19).

The critical path for the above project and the slack of P2 are, respectively,

  1. P1-P2-P4, 1 day
  2. P1-P3-P4, 1 day
  3. P1-P3-P4, 2 days
  4. P1-P2-P4, 2 days
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First calculate Estimated time Using formula : 
estimated=(optimistic+4*most likely+pessimistic)/6






To determine the Critical Path and conduct Critical Path Analysis, you need to:

  1.  create a Precedence Diagram.
  2. Define the duration of each activity.
  3. Identify all the paths.
  4. Calculate the duration of each path.
  5. Identify the longest path.

Here P1-P3-P4 is the longest path so it is critical path

Slack of an activity is the duration that it can slip by without delaying the subsequent task or completion of the project, or violating schedule constraint.

The simple 3-step process to calculate slack of ALL activities in your schedule network diagram –

Step 1: Arrange the paths in decreasing order of their total duration, starting with Critical path



Step 2: Find float for activities on the second longest path

This would be the difference between total duration of critical path and next longest path. In our example this would be               76-74=2 minutes. Assign this to ALL activities on this path, which do not already have a float. In this example that would be only activity.

Step 3: Do the same to all remaining paths, for unassigned activities

so slack time of p2=2


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ans c)
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Could you put up your solution please ??

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