$\backslash$table$[[$Activity$,,$Duration,$\backslash$table$[[$Preceding$],[$activities$]],\backslash$table$[[$Personnel$],[$required$]]],[\frac{?}{\text{b}\text{a}\text{r}}(A),$Purchase construction materials,$14$ weeks,$-,3],[$B$,$Purchase catering equipment,,,$],[$needed for new cafeteria,$2$ weeks,$-,2],[$C$,$Appoint supervisory architect,$2$ weeks,$-,1],[$D$,$Clear site,$3$ weeks,$-,3],[E,$Produce final building details,$7$ weeks,$C,D,1],[$F$,$Prepare site for construction,$2$ weeks,$E,2],[$G$,$Construct cafeteria,$13$ weeks,$A,F,5],[H,$Install utility services,$3$ 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,$4$ weeks,I,$L,3]]$

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

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