Kelle Carpet and Trim installs carpet in commercial offices. Peter Kelle has been very concerned with the amount of time it took to complete several recent jobs. Some of his workers are very unreliable. A list of activities and their optimistic completion time, the most likely completion time, and the pessimistic completion time (all in days) for a new contract are given in the following table:

Activity	Optimistic time (a)	Most likely time (m)	Pessimistic time (b)	Immediate predecessors
A	1	4	7	-
B	2	6	10	-
C	3	4	5	B
D	6	13	14	A
E	3	6	9	A, C
F	6	8	16	B
G	2	5	8	E, F

1. Draw the AON networks for these activities.

1. Filling out following table by calculating the expected time and variance for activities E and G.

Activity	Expected time	Variance
A	4	1
B	6	1.77
C	4	0.11
D	12	1.77
E	6	1
F	9	2.77
G	5	1

1. Using the expected time of each activity calculated in part (b) as the duration of the activity, determine the Early Start (ES), Early Finish (EF), Late Start (LS), Late Finish (LF), and slack for each activity. Fill out the table provided below with your findings.

Activity	ES	EF	LS	LF	Slack time
A	0	4
B	0	6
C
D
E
F
G	16	21	16	21	0

1. Determine the total project completion time and the critical path or paths for the project.

The total project completion time is 37.5 days.

1. Compute the total project variance and project standard deviation.

The project variance is 5.555555556and the project standard deviation is 2.357022604.

1. What is the probability that the project due date is between 18 and 20 days?

The probability for the project due date to be between 18 and 20 days is 0.328626759.

1. What is the due date that yield a 58% chance of completion?

The due date with a yield of 58% is 21.1575362.

1. What is the probability of completing Activity E by day 18?

1. Consider the path B-F-G. What is the probability that this path will exceed the expected project duration?

1. Assume there is a delay of 2 days on the expected time used in part (c) for activity F. How does this delay affect the project completion time? Now assume instead that there is a speed-up of 2 day on the expected time used in part (c) for activity F. How does this speed-up affect the project completion time?

1. What happens to the slack time of activity F if the expected time of Activity C is shortened by 1 day? Explain your answer.