Answered Essay: Using the activity table below, construct a CPM/PERT network noting the activity numbers and

Using the activity table below, construct a CPM/PERT network noting the activity numbers and durations. Identify the critical path through the network, determine the project completion time, and determine the slack time for each step.

Activity Predecessor Time (days)
1 15
2 7
3 2
4 5
5 3,4 4
6 5 3
7 1,2 8
8 2,6 12
9 3,7 2

Expert Answer

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Early start 1 = 0

Early finish = early start + activity time

Early finish 1 = 0 + 15 ( 15)

Early start 2 = 0

Early finish = 7

early start 3 = 0

early finish = 2

early start 4= 0

early finish = 5

early start 6 = early finish 5 ( 9)

early finish 6 = 9 + 3( 12)

early start 7 = maximum early finish ( 1,2) 15

early finish 7= 15 + 8 (23)

early start 8 = maximum early finish ( 2,6) 12

early finish 8 = 12 + 12 ( 24)

early start of 9 = maximum early finish (3,7) 23

early finish of 9 = 23+2 ( 25)

Latest finish of 9 = 25

Latest start of 9 = latest finish – activity time

latest start of 9 = 25 – 2 ( 23)

Latest finish of 8= 25

latest start of 8 = 13

latest finish of 7 = latest start of 9 ( 23)

latest start of 7 = 23 – 8 ( 15)

latest finish of 6 = latest start of 8 ( 13)

latest start of 6 = 13 – 3 ( 10)

latest finish of 5 = latest start of 6 ( 10)

latest start of 6 = 10 – 4 ( 6)

latest finish of 4 = latest start of 5 ( 6)

latest start of 4 = 6 – 5 ( 1)

latest finish of 3 = latest start of 5 ( 6)

latest start of 3 = 6 – 4 ( 2)

latest finish of 2 = latest start of 8 ( 13)

latest start of 2 = 13 – 6 ( 7)

latest finish of 1 = latest start of 7 ( 15)

latest start of 1 = 15 – 15 (0)

Activity Predecessor Time (days) Early start Early Finish Latest Start Latest finish Total Slack
1 15 0 15 0 15 0
2 7 0 7 6 13 6
3 2 0 2 4 6 4
4 5 0 5 1 6 1
5 3,4 4 5 9 6 10 1
6 5 3 9 12 10 13 1
7 1,2 8 15 23 15 23 0
8 2,6 12 12 24 13 25 1
9 3,7 2 23 25 23 25 0

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The critical path of the Network is 1- 7 – 9

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