For the following data:

Time (in Days)


Activity

Immediate Predecessor

Optimistic

Most Likely

Pessimistic

A



3

6

8

B



2

4

4

C



1

2

3

D

C

6

7

8

E

B, D

2

4

6

F

A, E

6

10

14

G

A, E

1

2

4

H

F

3

6

9

I

G

10

11

12

J

C

14

16

20

K

H, I

2

8

10







a. Draw the network diagram.
b. Calculate the expected (mean) completion time and its standard deviation for each activity.
c. Calculate the path mean and the path standard deviation for all of the possible paths.
d. Identify the critical path and critical activities.
e. What are the expected project completion time and variance?
f. What is the probability that the project:
i) will be completed within 38 days?
ii) will take more than 35 days to complete?
iii) will take between 35 and 38 days to complete?
Note: use the short method to compute the above probabilities.
g. Within how many days does the project have a 90% probability of completion?
h. Using the expected (mean) completion time, calculate the ES, EF, LS, LF, and slack for each activity.
i. Solve the problem using POM for Windows. Turn in the output that lists the activities and their ES, EF, LS, LF and the slack.
Notes:
1. Do parts (a) through (h) manually. Keep two decimal places for all calculations.
2. Disregard the network diagram generated by POM for Windows, because it uses different convention. To input the data, you will need the 'immediate predecessor' list for each activity. Furthermore, use the 'triple time estimates' option to input the activities and their estimated time durations. Make sure your manual computations in parts (b), (d), (e) and (h) match with the computer results.
3. Compute the probabilities manually, using the Normal table. Disregard the computer generated probabilities, if any.
4. Make sure your work looks nice and neat.
5. Answer parts (a) through (h) separately, with each section clearly marked.
6. Make sure that all pages are arranged serially.
7. The entire submission should be wordprocessed. That is, no handwritten works will be accepted.