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3. A portion of an activity network is shown in the figure; an arrow indicates t

ID: 3058396 • Letter: 3

Question

3. A portion of an activity network is shown in the figure; an arrow indicates the starting and ending of an activity. Activity C can start only after completion of both activities A and B, whereas activity D can start only after completion of C. A, B, C, D are statistically independent activities. The scheduled starting dates are as follows, and an activity cannot start earlier than its scheduled date. (For simplicity, assume all months have 30 days.) Activity A&B;: Activity C: Activity D: May 1 June1 August 1 The times required to complete each activity are Gaussian random variables as follows. Activity A: N(25 days, 5 days) Activity B: N(26 days, 4 days) Activity C: N(48 days, 12 days) Activity D: N(40 days, 8 days) Assume that both activities A and B started on schedule, that is, on May 1 Determine the probability that activity C will not start on schedule The availability of labor is such that unless C is started on schedule the necessary work force will be diverted to another project and thus will be unavailable for this activity for at least 90 days. What is the probability that activity D will start on schedule. Activity c Activity Activity B Moy l June l August I

Explanation / Answer

3. A portion of an activity network is shown in the figure; an arrow indicates the starting and ending of an activity. Activity C can start only after completion of both activities A and B, whereas activity D can start only after completion of C. A, B, C, D are statistically independent activities. The scheduled starting dates are as follows, and an activity cannot start earlier than its scheduled date. (For simplicity, assume all months have 30 days.) Activity A&B;: Activity C: Activity D: May 1 June1 August 1 The times required to complete each activity are Gaussian random variables as follows. Activity A: N(25 days, 5 days) Activity B: N(26 days, 4 days) Activity C: N(48 days, 12 days) Activity D: N(40 days, 8 days) Assume that both activities A and B started on schedule, that is, on May 1 Determine the probability that activity C will not start on schedule The availability of labor is such that unless C is started on schedule the necessary work force will be diverted to another project and thus will be unavailable for this activity for at least 90 days. What is the probability that activity D will start on schedule. Activity c Activity Activity B Moy l June l August I

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