A project network with 10 activities and 13 directed arcs is shown. Activity Start is connected to activity A and to activity B. Activity A is connected to activity C and to activity D. Activity B is connected to activity E. Activity C is connected to activity H. Activity D is connected to activity F and to activity G. Activity E is connected to activity F and to activity G. Activity F is connected to activity H. Activity G is connected to activity Finish. Activity H is connected to activity Finish. Activity Finish has no arcs directed to other activities. The following table lists the activity time estimates (in weeks) for each activity. Activity Optimistic Most Probable Pessimistic A 4 5 6 B 2.5 3 3.5 C 5 6 7 D 5 5.5 9 E 5 7 9 F 2 3 4 G 9 11 13 H 7 8 15 Based only on the critical path, what is the estimated probability that the project will be completed within the given time frame? (Round your answers to four decimal places.) (a) Within 21 weeks? (b) Within 23 weeks? (c) Within 27 weeks?

Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
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To help with preparations, a couple has devised a project network to describe the activities that must be completed by their wedding date.
A project network with 10 activities and 13 directed arcs is shown.
  • Activity Start is connected to activity A and to activity B.
  • Activity A is connected to activity C and to activity D.
  • Activity B is connected to activity E.
  • Activity C is connected to activity H.
  • Activity D is connected to activity F and to activity G.
  • Activity E is connected to activity F and to activity G.
  • Activity F is connected to activity H.
  • Activity G is connected to activity Finish.
  • Activity H is connected to activity Finish.
  • Activity Finish has no arcs directed to other activities.
The following table lists the activity time estimates (in weeks) for each activity.
Activity Optimistic Most Probable Pessimistic
A 4 5 6
B 2.5 3 3.5
C 5 6 7
D 5 5.5 9
E 5 7 9
F 2 3 4
G 9 11 13
H 7 8 15
Based only on the critical path, what is the estimated probability that the project will be completed within the given time frame? (Round your answers to four decimal places.)
(a)
Within 21 weeks?
 
(b)
Within 23 weeks?
 
(c)
Within 27 weeks?
 
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