Project Scheduling

The tasks with no slack time in a PERT (Program Evaluation Review Technique) chart are those that fall directly on the critical path. The critical path is a sequence of tasks that if delayed, would lengthen the overall project timeline. Thus, 'These tasks are on the critical path and delays can impact the project timeline' is the correct answer. Other answers are not correct: 'These tasks can be delayed without impacting the project timeline' is incorrect as no slack time means any delay will impact the project timeline. 'These tasks are not necessary for project completion and could be removed' is incorrect because tasks on the critical path are generally necessary for the project's completion. And lastly, 'This means your PERT chart is incorrectly charted and needs correction' is wrong because the appearance of tasks with no slack time does not imply an incorrectly charted PERT.

In a project, a float is a period that a task in a project can be delayed without causing a delay to subsequent tasks or the project as a whole. Since the critical task was delayed for 2 days, but had a float of 3 days, it means that there is still one day left within which the task can be delayed without affecting the project finish date. Thus, the correct answer is 'The project finish date remains unaffected.'
The answer 'The project finish date is delayed by 2 days.' is incorrect because the project float covers this delay. The answer 'The project finish date is advanced by 3 days.' is incorrect as the delay doesn’t accelerate the project schedule, it consumes the buffer time. The answer 'The project finish date is delayed by 3 days.' is also incorrect as the delay doesn’t exceed the project float.

The course of action should address the issue on the critical path, which is the sequence of project activities that adds up to the longest overall duration. If there's a delay in one task on this path, it considerably impacts the whole project timeline. The best way to handle this situation is to identify possible ways to fast track other tasks to make up for the delay. This involves reviewing other tasks on the critical path and identifying where efficiencies can be made, or more resources can be allocated to offset the delay. On the other hand, ignoring the delay and continuing with the project as scheduled wouldn't solve the problem but may complicate further more the project timeline. Revision of the whole PERT chart is unnecessary because only tasks on the critical path will directly impact the project timescale. And lastly, adding more resources to non-critical tasks won't necessarily recover the time lost on the project's critical path.