Project scheduling (CPM): Which of the following statements about slack, cost minimization, and the critical path is correct?

Introduction / Context:
Critical Path Method (CPM) is a deterministic project scheduling tool. It highlights the sequence of activities that governs the total project duration and quantifies schedule flexibility through slack (float). Understanding slack, the definition of the critical path, and CPM’s role in cost optimization is essential for project planning and control.

Given Data / Assumptions:

• A well-defined activity-on-node or activity-on-arrow network with durations.
• Earliest and latest times computed by forward and backward passes.
• Direct costs rise when activities are crashed; indirect costs accrue per unit time of project duration.

Concept / Approach:
Total slack of an activity equals LS − ES or LF − EF. Activities with zero slack are critical; delaying them delays the entire project. The critical path is the longest-duration path through the network, and thus yields the minimum possible project time if no durations are reduced. CPM cost trade-off (crashing) compares extra direct cost to the reduction in indirect cost to minimize total cost.

Step-by-Step Solution:

Verification / Alternative check:
Any delay in a zero-slack activity increases project duration 1:1. Cost curves typically show a convex trade-off where an optimal crash point minimizes total cost.

Why Other Options Are Wrong:
Each individual statement (a), (b), and (c) is true; therefore “all of the above” is the only fully correct choice.

Common Pitfalls:
Confusing free float with total slack; assuming noncritical activities cannot become critical after crashing; crashing noncritical activities first (ineffective for duration reduction).

Final Answer:
all of the above