1. Consider the table of tasks, immediate predecessors and estimated task time below:

Activity	Immediate Predecessor	estimated task time	Slack
A	--	6
B	--	4
C	A	10
D	A	6
E	B	4
F	D, E	2
G	D, E	7
H	C, F	6

A) Draw the project diagram. Please try to keep it right-side up so that we can grade it easily. Use as much paper as you need, as long as the diagram is clear.

B) What is the critical path?

C) Determine the slack for each task. Show your work below. Enter your answer in the table above.

2.Now that COVID is more under control than previously, suppose at a local venue a production manager is preparing to put on its first rock concert of the summer. The tasks needed to produce the concert are given in the table below:

Activity	Description	Immediate Predecessor	estimated task time	Slack
A	Negotiate contract with musicians	--	15
B	Reserve site	--	10
C	Manage travel plans for groups	A	5
D	Screen and hire security personnel	B	7
E	Arrange advertising and ticketing	B, C	10
F	Hire parking staff	D	5
G	Arrange concession sales.	E	5

A) Draw the project network diagram. (Use as much paper as you need, but try to draw right side up for grading.

B) Determine the critical path.

C)For each of the tasks, determine the slack. Show your work for each task. Enter your answer in the table above.

3. ISO is an independent, non-governmental international organization with a membership of 163 national standards bodies. International Standardsgive world-class specifications for products, services and systems, to ensure quality, safety and efficiency. They are instrumental in facilitatinginternational trade.

A direct auto-parts supplier for a car manufacturer is trying to gain a competitive advantage and meet quality requirements of its customers. It has decided to see ISO certification for the development of its quality management system. It is seeking continued improvement in preventing defects and reducing process variation and waste.The project management team has developed the following set of required activities, along with estimated times, to achieve ISO certification.

Activity	Description	Immediate Predecessor	Time estimates (weeks)
a	m	b	Average	Variance
A	Appointment of company task force	--	1	2	3
B	Development of feasibility plan	A	2	3	4
C	selection of third party registrar and auditor	B	1	2	3
D	Development of quality manual, procedure, and instruction documents	B	10	14	20
E	Quality system training for all employees	B	4	7	10
F	Outside training for company quality managers and internal plant auditors	B	4	7	10
G	Plant preparation and organization to meet ISO 9001 standards, including the use of SPC charts to identify non-conforming processes.	C	18	24	32
H	Preparation of ISO application documents with outside auditor, set schedule for submissions to registrar	C	4	6	10
I	Internal audit of plant	D,F,H,G	10	12	16
J	Corrective action plans for necessary process improvements	I	8	12	20
K	Outside auditor visit and audit	J	1	2	3
L	Corrective action plans developed based on auditor report and implemented	K	2	4	5
M	Follow up visit and re-audit by auditor	L	1	2	4
N	Auditor recommendation to registrar for the ISO certification	M	1	2	2

A) Calculate the average time to complete each activity and put your answers in the above table. You do not need to show all your work, however, show the work for the following activities below as exemplar calculations: A, G, N

B) Construct the network diagram for this project. Fill in the activity, activity time, earliest start and finish, latest start and finish for each node. Please use another sheet of paper for the diagram. If you need more horizontal space, it is acceptable to put small circle nodes with numbers at the right hand side of one part of the diagram, and corresponding small circle nodes with numbers at the left hand side of the continuation of the diagram. Most importantly, make sure it is legible and readable. I give our TA permission NOT to grade anything she cannot easily read.

C) What is the critical path, and how long will the project take on average?

D) Calculate the overall variance of the project time by calculating the appropriate activity variances and summing them. Fill in those variances in the table. Below, please choose the FIRST TWO of the activities you need, and show how you calculated those variances below.

E) What is the probability that the certification project can be completed within 1 year? (show your work)

F) What is the probability that the certification project can be completed within 1 year? (show your work)

G) What is the 95^th percentile of project completion time? (Show work)