Explain PERT and calculate the critical path and its duration.

Okay Michou, let's break down question 8.

8. (i) (a) The full meaning of the acronym PERT is Program Evaluation and Review Technique.

8. (i) (b)

• Advantage: PERT charts provide a visual representation of project tasks and their dependencies, helping in better planning and scheduling of complex projects, especially when activity durations are uncertain.
• Disadvantage: They can be time-consuming and complex to create and maintain for very large projects, and the accuracy of the project duration relies heavily on the accuracy of individual task duration estimates.

8. (i) (c) To calculate the critical path, we find the longest path through the network.
Let's list all possible paths from A to I and their durations:

• Path 1: A $\to$ B $\to$ G $\to$ I = $3 + 3 + 4 = 10$
• Path 2: A $\to$ B $\to$ C $\to$ F $\to$ H $\to$ I = $3 + 1 + 2 + 3 + 2 = 11$
• Path 3: A $\to$ B $\to$ C $\to$ E $\to$ H $\to$ I = $3 + 1 + 4 + 1 + 2 = 11$
• Path 4: A $\to$ C $\to$ F $\to$ H $\to$ I = $2 + 2 + 3 + 2 = 9$
• Path 5: A $\to$ C $\to$ E $\to$ H $\to$ I = $2 + 4 + 1 + 2 = 9$
• Path 6: A $\to$ D $\to$ H $\to$ I = $6 + 1 + 2 = 9$

The longest duration is 11.
The critical paths are A $\to$ B $\to$ C $\to$ F $\to$ H $\to$ I and A $\to$ B $\to$ C $\to$ E $\to$ H $\to$ I.
The critical path duration is $\boxed{\text{11 units}}$.

8. (i) (d) To calculate the slack time for tasks B, F, and E, we first determine the Earliest Event Times (EET) and Latest Event Times (LET) for each node.

Earliest Event Times (EET):

• EET(A) =