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# Determining the critical path

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Dave Fletcher (see Problem 3.10) was able to determine the activity times for constructing his laser scanning machine. Fletcher would like to determine ES, EF, LS, LF, and slack for each activity. The total project completion time and the critical path should also be determined. Here are the activity times:

ACTIVITY TIME (WEEKS) ACTIVITY TIME (WEEKS)
A 6 E 4
B 7 F 6
C 3 G 10
D 2 H 7

Data from Problem 3.10
IMMEDIATE IMMEDIATE
ACTIVITY PREDECESSOR,(S) ACTIVITY PREDECESSOR(S)
A - E B
B - F B
C A G C, E
D A H D, F

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#### Solution Summary

This solution determines the critical path and project completion time in the given case.

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## Determining Normal and Crash Critical Paths

Activity Normal time Crash time Normal cost Crash cost
1-2 3 2 1000 1500
2-3 4 2 2000 4000
2-4 4 3 2500 3500
3-5 3 1 1500 2500
4-5 4 2 6000 12000
5-6 6 3 2000 5000

Determine:
a) Normal critical path.
b) Crash critical path.
c) The first and last activities to be crashed.
d) Minimum project completion time with the least increase in the cost over normal costs.
e) The minimum completion time, assuming a budget of \$23,500.
f) The minimum cost to complete the project in 12 weeks.

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