Question

A project consists of five activities (A, B, C, D, E). Each activity duration follows beta distribution. Three-time estimates are given and expected completion time is __________ weeks (in integer).

Hint:

Longest expected-time path in the network determines the project duration.

Answer 1

Correct Answer: 15

For each activity, the expected time using PERT is \[ t_e = \frac{a + 4m + b}{6} \] Compute for each activity: A:
\[ t_e = \frac{4 + 4(5) + 6}{6} = \frac{30}{6} = 5 \] B:
\[ t_e = \frac{1 + 4(3) + 5}{6} = \frac{18}{6} = 3 \] C:
\[ t_e = \frac{1 + 4(2) + 3}{6} = \frac{12}{6} = 2 \] D (depends on C):
\[ t_e = \frac{2 + 4(4) + 6}{6} = \frac{24}{6} = 4 \] E (depends on B and D):
\[ t_e = \frac{3 + 4(4) + 5}{6} = \frac{24}{6} = 4 \] Now determine the critical path: Paths: 1. A → B → E: \[ 5 + 3 + 4 = 12 \] 2. A → C → D → E: \[ 5 + 2 + 4 + 4 = 15 \] Critical path = A–C–D–E, duration = 15 weeks. Thus, \[ \boxed{15\ \text{weeks}} \]