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Let’s start with Part A, using the estimates for Company A:
A1. Expected Completion Time for Each Activity:
For each activity, you’ll calculate the expected completion time using the formula for expected time:
[ TE = \frac{O + 4M + P}{6} ]
Where ( O ) is the optimistic time, ( M ) is the most likely time, and ( P ) is the pessimistic time.
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A2. Variance for Each Activity:
The variance for each activity can be calculated using the formula:
[ \text{Variance} = \frac{(P – O)^2}{36} ]
A3. PERT Chart and Critical Path:
Using the expected completion times calculated in A1, create a PERT chart showing all activities and their expected times. Then, identify the critical path by determining the longest path through the network diagram.
A4. Additional Calculations:
a. Expected duration of the entire project: The sum of expected completion times along the critical path.
b. Slack for Activity E: The difference between its latest start time and earliest start time.
c. Slack for Activity C: The difference between its latest start time and earliest start time.
d. Earliest start time for Activity F: The earliest time it can start considering the dependencies.
e. Latest finish time for Activity G: The latest time it must finish without delaying the project.
A5. Probability of Completing Project in 48 Weeks:
To find this, you’ll use the concept of Z-scores. First, find the standard deviation of the project duration, then find the Z-score using the formula:
[ Z = \frac{48 – TE}{\text{Standard Deviation}} ]
Then, use a Z-table to find the probability associated with the Z-score.
For Part B and C, follow similar steps using the data for Company B, considering crashing options and their associated costs to meet the given criteria.
Let’s start with Part A, and if you have any specific questions or need further clarification on any step, feel free to ask!
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