$\backslash$table$[[,,\backslash$table$[[$Preceding$],[$Activity$]],\backslash$table$[[$Personnel$],[$required$]],],[$A$,$Purchase construction materials,Duration,,$],[$B$,$Purchase catering equipment,,$-,3],[,$needed for new cafeteria,$2$ weeks,$-,],[$C$,$Appoint supervisory architect,$2$ weeks,$-,2],[$D$,$Clear site,$3$ weeks,$-,1],[$E$,$Produce final building details,$7$ weeks,C$,$ D$,3],[$F$,$Prepare site for construction,$3$ weeks,E$,1],[$G$,$Construct cafeteria,$13$ weeks,A$,$ F$,2],[$H$,$Install utility services,$5$ weeks,G$,2],[$I$,$Install catering equipment,$5$ weeks,B$,$ H$,2],[$J$,$Decorate internally,$2$ weeks,B$,$ H$,2],[$K$,$Stock cafeteria,$2$ weeks,I, J$,1],[$L$,$Hire catering staff,$9$ weeks,$-,2],[$M$,$Train staff on site,$5$ weeks,I, L$,3]]$

$($a$)$ Identify the critical path.

$($b$)$ Determine float times for all activities.