Network Analysis PERT and CPM Questions and Answers

Answer: C

The critical path is a - d - f - h.

List every path through the network and its duration:

• a - b - e - g - h: 3 + 4 + 2 + 6 + 2 = 17 days
• a - c - g - h: 3 + 5 + 6 + 2 = 16 days
• a - d - f - h: 3 + 4 + 9 + 2 = 18 days

The longest path, 18 days, is the critical path and fixes the project duration.

a - b - e - g - h and a - c - g - h are real paths with slack of 1 and 2 days. a - b - c - f - h is not a path at all: c does not follow b, and f follows d, not c.

Answer: A

The critical path remains the same and the total duration changes to 19 days.

Activity f lies on the critical path a - d - f - h, so lengthening it by one day lengthens that path to 3 + 4 + 10 + 2 = 19 days. The other paths (17 and 16 days) are unchanged and still shorter, so the critical path is still a - d - f - h.

Any change to a critical activity changes the project duration, so 'total duration remains the same' is wrong. The critical path would change only if another path became the longest, and 17 days is the length of a non-critical path, not the new project duration.

Answer: B

CPM is a deterministic model, as the key states. In the critical path method the durations of activities are known and fixed, so there is no uncertainty, while PERT uses three time estimates (optimistic, most likely and pessimistic) for each activity, and so it is a probabilistic model. The options that name PERT or both, or neither, are wrong.

Answer: B

The latest finish time for G is 10 hours.

Forward pass (earliest finish): A 2, B 3, C 2; D 6, E 8, F 7, G 5; H starts after D and E, so finishes at 8 + 10 = 18; I 12; J 13; K starts after H, I and J, at 18, and finishes at 21. The project takes 21 hours along the critical path B-E-H-K.

Backward pass: K must finish by 21, so it starts by 18; J must therefore finish by 18 and start by \(18 - 8 = 10\). G is J's only predecessor, so G must finish by 10 hours.

5 is G's earliest finish, 8 confuses it with J's duration, and 9 has no basis. G has 5 hours of slack, so it is not critical.