$\backslash$table$[[$Activity$,,$Duration,$\backslash$table$[[$Preceding$],[$activities$]],\backslash$table$[[$Personnel$],[$required$]]],[$A$,$Purchase construction materials,$11$ weeks,$-,3],[$B$,\backslash$table$[[$Purchase catering equipment$],[$needed for new cafeteria$]],,-,2],[$C$,\backslash$table$[[$needed for new cafeteria$],[$Appoint supervisory architect$]],\backslash$table$[[2$ weeks$],[2$ weeks$]],\backslash$table$[[-],[-]],1],[$D$,$Clear site,$3$ weeks,$-,3],[$E$,$Produce final building details,$9$ weeks,C$,$ D$,1],[$F$,$Prepare site for construction,$2$ weeks,E$,2],[$G$,$Construct cafeteria,$12$ weeks,$A,F,5],[$H$,$Install utility services,$3$ weeks,G$,2],[$I$,$Install catering equipment,$4$ weeks,B$,$ H$,2],[$J$,$Decorate internally,$2$ weeks,$B,H,2],[$K$,$Stock cafeteria,$2$ weeks,$1,J,1],[$L$,$Hire catering staff,$7$ weeks,$-,2],[M,$Train staff on site,$3$ weeks,I,$L,3]]$

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

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

$($D$)$

$\backslash$table$[[$Activity$,$Duration,Hoat$],[1,11,$