Problem $1$

Consider the set of activities, durations $($in days$),$ and predecessors for the project in the table below:

$\backslash$table$[[$Activity$,$A$,$B$,$C$,$D$,$E$,$F$,$G$],[$Duration$,3,5,2,4,6,3,2],[$Predecessors$,-,-,$A$,$B$,$ C$,$A$,$C$,$ E$,$B$]]$

Develop a dependency diagram representing the project's activities.

Identify all paths to project completion.

Determine the critical path$($s$)$ and the total project duration.