A business organisation is trying to improve staff morale and motivation and has decided to replace the existing staff canteen with a modern cafeteria. The works department has drawn up a detailed list of the various activities that will need to be completed, together with an estimate of how long each activity will take and the sequencing of activities. This information is shown in the following table.

$\backslash$table$[[$Activity$,,$Duration,$\backslash$table$[[$Preceding$],[$activities$]],\backslash$table$[[$Personnel$],[$required$]]],[\frac{?}{\text{b}\text{a}\text{r}}(A),$Purchase construction materials,$11$ weeks,$-,3],[$B$,\backslash$table$[[$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,$9$ weeks,$C,D,1],[$F$,$Prepare site for construction,$2$ weeks,E$,2]]$

$($a$)$ The critical path is D$-$E$-$F$-$G$-$H$-$I$-$M $.$

$($b$)$

$\backslash$table$[[$Activity$,$Duration,Float$],[$A$,11,],[$B$,2,],[$C$,2,],[$D$,3,],[$E$,9,],[-,-,],[,,]]$

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