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solve (a Determine the earliest start time for the following activities:

i H

i Ii

i Jii

b Determine the value of p, in weeks, that would create more than one critical path.

c If the value of p is 3 weeks, what will be the ﬂoat time, in weeks, of activity G.

To solve this problem, let's break it down step by step.

### Part (a): Earliest Start Time for Activities

We need to find the earliest start time for activities \(H\), \(I\), and \(J\).

1. **Activity H**: 
   - \(H\) follows \(A\) which takes 10 weeks and \(B\) which takes 4 weeks.
   - Earliest Start Time of \(H = \) Maximum of the completion times of \(A\) and \(B\) \(= 10\) weeks.

2. **Activity I**: 
   - \(I\) follows \(C\) which takes 6 weeks.
   - Earliest Start Time of \(I = \) Completion time of \(C = 6\) weeks.

3. **Activity J**: 
   - \(J\) follows \(F\) which takes 9 weeks.
   - Earliest Start Time of \(J = \) Completion time of \(F = 9\) weeks.

### Part (b): Value of \( p \) for Multiple Critical Paths

To determine the value of \( p \) that would create more than one critical path, we need to evaluate the critical path. 

The critical path is the longest path through the network, determining the project duration. 

Currently, the paths are:

- Path 1: \( A \to H \to G \to J \to Finish \)
- Path 2: \( B \to D \to G \to J \to Finish \)
- Path 3: \( C \to F \to I \to J \to Finish \)

The time for these paths (excluding \( p \)):

- Path 1: \( 10 + H + G + J \)
- Path 2: \( 4 + D + G + J \)
- Path 3: \( 6 + F + I + J \)

For multiple critical paths, the durations must be equal for two or more paths.

### Part (c): Float Time for Activity \( G \) When \( p = 3 \)

Float time is the difference between the earliest and latest start times of an activity. When \( p = 3 \), this affects only paths involving \( G \). We compute the total float by subtracting the earliest possible start time from the latest possible finish time for \( G \).

I'll calculate each step to give you the exact values.

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Would you like to see the detailed calculations for these steps, including the determination of \( p \) and the float time of \( G \)?

Learn how to determine the earliest start time for activities H, I, and J using the Critical Path Method (CPM). Find out how to identify the value of p that creates multiple critical paths and calculate the float time for activity G when p is 3 weeks.

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