Quick questions on Critical path analysis: precedence tables and minimum project duration for HSC Maths Standard 2

From this table, you build the network.

Some precedence tables cannot be drawn with real activities alone. A dummy activity is a zero-duration edge (drawn dashed) that carries a precedence relationship without representing any real work. Two situations force one:

Turning a precedence table into a network is the part students find hardest. Below, the network shown at the top of this page is built one stage at a time, with the reasoning spelled out at each step.

A path is a sequence of activities from the project start to the project end. The length (duration) of a path is the sum of its activity durations.

The critical path is the longest path through the network. Its length is the minimum possible project duration. No matter how you schedule the activities, the project cannot finish faster than the critical-path length, because that run of activities must happen in order.

If two or more paths tie at the longest length, every one of them is critical, and every activity lying on any of them is a critical activity. Ties are common in exams and easy to miss if you stop at the first long path you find.

Every non-critical activity has float (slack): the amount it can be delayed without pushing out the project end date. Float is computed from the forward and backward scan (the next dot point), but the headline result belongs here because it is what decides whether an activity is critical.