A project involves the activities shown below (activity times, standard deviation associated with each activity, and immediate predecessor(s) for each activity are also shown). The data are in weeks.

As we discussed in the class, the environment of a project can be either deterministic or probabilistic. If it is probabilistic then, according to convention, the analyst is required to give three different time estimates for completing each activity. These time estimates are usually denoted by: a (most optimistic time), m (most likely time), and b (most pessimistic time).

The expected time for an activity is the weighted average of the three estimates. A weight of 1 is assigned to a, 4 to m, and 1 to b and the expected time for each activity is then calculated by:

t_{i =} (a + 4m + b) /6

Further, it is also possible to estimate a standard deviation for each activity as follows:

_{i =} (b - a)/6

Please keep the above two relationships in mind while answering all questions.

ACTIVITY EXPECTED TIME STD. DEVIATION IMM. PREDECESSOR

A 12 1 None

B 10 1 None

C 8 1 None

D 14 1 B

E 6 1 C

F 18 2 B, A

G 11 1 D, E

H 21 3 C

I 7 1 F, G

Q5. The maximum path slack in this network is:

a) 12 weeks

b) 8 weeks

c) 10 weeks

d) 9 weeks

e) None of the above

Q# 6. The length of the critical path in this network is:

a) 24 weeks

b) 35 weeks

c) 32 weeks

d) 30 weeks

e) None of the above

Q# 7. For activity A, the value of m =12; and b = 15. Then, the most optimistic time a for activity A is:

a) 4 weeks

b) 5 weeks

c) 9 weeks

d) 7 weeks

e) None of the above

Q# 8. The EF (earliest finish time) for activity G is:

a) 16 weeks

b) 24 weeks

c) 21 weeks

d) 8 weeks

e) None of the above

Q# 9. The probability that the project will take more than 27 weeks is:

a) More than 14% but less than or equal to 18%

b) More than 18% but less than or equal to 20%

c) More than 20% but less than or equal to 22%

d) More than 22% but less than 24%

e) None of the above