Critical Path Method (CPM): In a project network, the critical path represents which of the following for overall project completion?

Introduction / Context:
Critical Path Method (CPM) identifies the longest path of dependent activities in terms of duration. This path determines the shortest possible time in which a project can be completed because any delay on the critical path directly delays project finish.

Given Data / Assumptions:

• A network of activities with deterministic durations.
• Logical precedence constraints are respected.
• No resource constraints are considered in the baseline CPM calculation.

Concept / Approach:
The critical path is the path with zero total float and the greatest cumulative duration among all paths. Project duration equals the duration of this path; thus it represents the minimum achievable completion time given current logic and durations.

Step-by-Step Solution:
List all start-to-finish paths.Sum durations along each path.Identify the path with the greatest sum; this is the critical path.Project completion time equals this sum; therefore it is the minimum feasible time unless logic or durations change.

Verification / Alternative check:
Forward pass gives earliest finish of the final event; backward pass confirms zero float on critical activities. Any compression must target critical activities (crashing) to reduce project duration.

Why Other Options Are Wrong:

• Maximum time: misleading; the critical path duration is the minimum achievable project completion time.
• Maximum/minimum cost: CPM by itself does not determine cost.
• Maximum float: critical path has zero float.

Common Pitfalls:
Confusing 'longest path' in duration with 'maximum time' as a goal; assuming that noncritical activities can be delayed without consequence beyond their float.

Final Answer:
minimum time