Draw a path diagram for the project. 2. Calculate the expected length and variance of each task. Fill in the following worksheet.

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CPM/Pert analysis

The Cosmic project consists of 8 interdependent tasks, labeled A through H. You’ve consulted experts, and have determined an optimistic, likely and pessimistic completion time (in months) for each of the tasks. The dependencies, and the times, are listed below.

Task	Precursor(s)	Optimistic	Likely	Pessimistic
A	(start)	1	3	5
B	(start)	2	4	7
C	A	4	7	9
D	A	1	4	5
E	A	3	5	6
F	D,E	1	2	4
G	B	3	8	10
H	C,F,G	1	2	4
(end)	H

1. Draw a path diagram for the project.

2. Calculate the expected length and variance of each task. Fill in the following worksheet.

Task	Optimistic (O)	Likely (L)	Pessimistic (P)	Expected Task	Task Variance
A	1	3	5
B	2	4	7
C	4	7	9
D	1	4	5
E	3	5	6
F	1	2	4
G	3	8	10
H	1	2	4

3. Use the following worksheet to determine the lengths of all possible paths. Determine the critical path, its variance, and standard deviation.

What is the critical path? What is its length?

Path	Expected Path	Path Variance	Path Standard Deviation

4. What is the probability of completing the project in 16 months? Show your intermediate results in the worksheet below.

Path			Target path length ET		Cumulative probability of Z1

Note: (1) Determine from a Z-to-p table, or by using an online converter; i.e., http://sampson.byu.edu/courses/z2p2z-calculator.html

The Magus Project consists of 12 interrelated tasks, A through L. Their estimated normal completion times, normal costs, crash times and crash costs are given below. (Times in weeks; costs in thousands of dollars.)

Task	Predecessors	Normal Time	Normal Cost	Crash Time	Crash Cost
A	(start)	3	20	2	25
B	(start)	7	30	5	50
C	(start)	4	10	3	12
D	A,B	3	2	2	5
E	B,C	8	27	7	33
F	C	6	8	4	10
G	C	7	9	5	12
H	A	4	6	2	8
I	A,D	3	10	1	12
J	E	3	10	1	12
K	F,G	6	8	5	9
L	J,K	5	7	4	8

Use an online application (e.g., Sporkforge, 2014) to find the critical path. Copy the output of the app into your upload as an image.

5. Which tasks are on the critical path?

6. What is the expected completion time of the project?

Instead of being finished in 7 weeks, task B requires 9 weeks.

7. Which (if any) tasks should be crashed, to make up the lost time? Why?

8. What is the additional cost of crashing the project?

Assignment Expectations

• For Part 1; Draw a PERT-CPM diagram clearly showing all the paths, plus the critical path. You may draw the diagram by hand, and paste a scanned image into your upload, but it must be totally legible.
• For Part 2; A PERT-CPM diagram is not required. Use an online app; paste an image of the app output into your paper.
• Show, and explain, all the calculations supporting your answers.
• Unambiguously state your answers.

General Case Expectations

• Follow the instructions in the BSBA Writing Style Guide (July 2014 edition), available online at https://mytlc.trident.edu/files/Writing-Guide_Trident_2014.pdf.
• There are no guidelines concerning length. Write what you need to write – neither more, nor less.
• Clearly demonstrate your understanding of both the theory covered in the Module, and the particulars of the Case.
• Provide references and citations. At a minimum, you should reference the course materials. These are referenced in APA format on the Background Info page.