Practice Question: Length of an Activity Based on Critical Path

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Solution

Answer: C) 9 days

A project’s critical path is the minimum length it takes to complete the schedule. 
If the critical path is based on the total length of activities AEG, then the total maximum length of activities ADF will be one less than the length of AEG.

Total Length of AEG:
$$ AEG\ =\ 15\ days\ +\ 7\ days\ +\ 12\ days\ =\ 34\ days $$
Maximum Length of ADF (to keep AEG as the critical path):
$$ ADF\ =\ AEG-1=33\ days $$
Solving for Maximum Length of Activity D:
$$ 33\ days=A+D+F $$
$$ 33\ days=15\ days+D+9\ days $$
$$ D=9\ days $$
 

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