Problem 1.

Draw the network and identify the critical path.

Calculate the earliest-latest starting and finishing times for each activity.

Also, calculate Activity Slack times for each activity.

Activity	Preceding Activity	Time in Weeks
A	-	7
B	-	8
C	-	6
D	A	6
E	B	6
F	B	8
G	C	4
H	D, E	7
I	F, G, H	3

Problem 2.

Draw the network and identify the critical path.

Calculate the earliest-latest starting and finishing times for each activity.

Also, calculate Activity Slack times for each activity.

Activity	Preceding Activity	Time in Weeks
A	-	4
B	-	6
C	A, B	7
D	B	8
E	B	5
F	C	5
G	D	7
H	D, E	8
I	F, G, H	4

Problem 3.

Consider the following network (all times are in days)

1. Drawn an activity-on-arrow network diagram representing the project.
2. identify the critical path and associated time.
3. What is the Network Slack time assuming the customer specification calls for the project to be completed in 21 days?
4. Calculate the Event Slack for all events not on the critical path.
5. What is the expected time for 68, 95, and 99 percent completion limits (i.e. the range)?
6. Calculate the numbers of days needed to obtain a 75% confidence level the project will be complete by.

Activity	Initial Node	Final Node	Optimistic Time Estimate	Pessimistic Time Estimate	Most Likely Time Estimate
A	1	2	1	3	2
B	1	4	4	6	5
C	1	3	4	6	5
D	2	6	2	4	3
E	2	4	1	3	2
F	3	4	2	4	3
G	3	5	7	15	9
H	4	6	4	6	5
I	4	7	6	14	10
J	4	5	1	3	2
K	5	7	2	4	3
L	6	7	6	14	10

Problem 4.

Draw the network and identify the critical path.

Job Activity	Initial Node	Final Node	Estimated Time
A	1	2	2
B	1	3	3
C	1	4	3
D	2	5	3
E	2	9	3
F	3	5	1
G	3	6	2
H	3	7	3
I	4	7	5
J	4	8	3
K	5	6	3
L	6	9	4
M	7	9	4
N	8	9	3
O	9	10	2

Problem 5.

On May 1^st, the PM sent a memo to their boss stating that Project X would require 13 weeks to complete (see network logic below activity on node diagraming) at a total project cost of $62K.

Unknown to the PM, there was a contract executed whereby it was was agreed that there would be a $5K penalty payment per week for every week the project exceeds six (6) weeks.

As such, the PM developed the following costing (all costs are in Ks) and timing matrix (all timings are in weeks).

Normal				Crash
Activity	Time	Cost		Time	Cost	Additional Cost per Week
A	3	$6		2	$8	$2
B	5	$12		4	$13.5	$1.5
C	5	$16		3	$22	$3
D	4	$8		2	$10	$1
E	2	$6		1	$7.5	$1.5
F	3	$14		1	$20	$3
	Total	$62

What is the minimum amount of additional funding (beyond the project budget of $62K) the PM should request (given the contractual penalty provision)?