The activities of a project, their duration and the precedence relationships are given in the table. For example, in a precedence relationship “X < Y, Z” means that X is predecessor of activities Y and Z. The time to complete the activities along the critical path is ________ weeks

Activity	Duration (Weeks)	Precedence Relationship
A	5	A<B,C,D
B	7	B<E,F,G
C	10	C<I
D	6	D<G
E	3	E<H
F	9	F<I
G	7	G<I
H	4	H<I
I	2	---

Correct Answer: The correct option is 23 (or the option corresponding to 23).

Step-by-step Explanation:

To determine the time required to complete the activities along the critical path, we first analyze the precedence relationships and durations of each activity as shown in the project table:
1. Activity A has a duration of 5 weeks and acts as a predecessor to activities B, C, and D (written as $A<B,C,D$). Since it has no predecessor, it is the starting activity.
2. Activity B (duration 7 weeks) precedes E, F, and G.
3. Activity C (duration 10 weeks) precedes I.
4. Activity D (duration 6 weeks) precedes G.
5. Activity E (duration 3 weeks) precedes H, which (duration 4 weeks) precedes I.
6. Activity F (duration 9 weeks) precedes I.
7. Activity G (duration 7 weeks) precedes I.
8. Activity I (duration 2 weeks) has no successor, indicating it is the final activity of the project.

By tracing the dependencies from the starting activity (A) to the final activity (I), we can identify all possible paths through the network and compute their total durations:

Path 1: A → B → E → H → I
Duration:

$5+7+3+4+2=21\text{weeks}$

Path 2: A → B → F → I
Duration:

$5+7+9+2=23\text{weeks}$

Path 3: A → B → G → I
Duration:

$5+7+7+2=21\text{weeks}$

Path 4: A → C → I
Duration:

$5+10+2=17\text{weeks}$

Path 5: A → D → G → I
Duration:

$5+6+7+2=20\text{weeks}$

The critical path is defined as the sequence of dependent tasks that determines the minimum time needed to complete the project, which is the path with the longest total duration.

Comparing the durations of all paths, we find that Path 2 (A → B → F → I) has the maximum duration of 23 weeks. Therefore, the critical path duration is 23 weeks.