The purpose of determining the critical path on a PERT network is to:

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The critical path is the sequence of tasks that takes the longest to complete and determines the overall duration of the project. It identifies the tasks that are critical to the project's completion and helps project managers optimize their resources accordingly. Estimating a payment schedule or finding the most expensive sequence of events are not the main purposes of determining the critical path. Establishing a delivery schedule for just-in-time inventory may be a consequence of knowing the project's critical path, but it is not its primary purpose.

The Purpose of Determining the Critical Path on a PERT