(a) Given that an activity takes generally 20 minutes to perform while the optimistic and pessimistic estimates of its performance are, respectively, one-half and thrice this time, answer the following: (i) What is the expected duration of this activity? (ii) What is its variance? (iii) In scheduling the project, of which this activity is a part, how much time should be provided for this activity?

(b) You are given the following information about a project:

(i) Draw the network, obtain the scheduling times of various activities, and calculate their total and free slacks.
(ii) Obtain the critical path and find the duration of the project.
(iii) Activities 2- 6 and 4- 5 can each be speeded up and reduced by two days at no cost. Do you think it is worthwhile to reduce these times in terms of the completion time of the project?

(c) Assume that for the project given in (b), the activity durations given represent their expected durations. It is further given that variance along the critical path is 81 days2• What is the probability of completing the project in 33 days? 44 days?

Transcribed Image Text:

111 312 Activity 1-2 Duration (days) Activity Duration (days) 4 2-6 18 1-3 7 3-5 10 10 3-6 16 3 4-5 9 2-4 8 5-6 6 2-5 11 5-7 11 6-7 8