You are managing the project described in the table below. The activities and their predecessors are given, together with the duration and resource requirement of each activity. $A$ is the initial activity and I is the completion activity.

$\backslash$table$[[$activity$,$predecessors,duration,Resource,$],[$A$,,4,8,\backslash$table$[[$A and B are$],[$the initial activities$]]],[$B$,,2,2,],[$C$,$A$,$B$,4,6,],[$D$,$A$,$B$,2,2,],[$E$,$C$,2,2,],[$F$,$D$,$C$,2,8,],[$G$,$E$,2,4,],[$H$,$F$,$G$,2,3,],[$I$,$F$,$G$,2,3,],[$J$,$I,$6,5,\backslash$table$[[$J and K are$],[$K$]]],[$H$,$I,$4,2,$Terminal events,$]]$

$($a$)$ Construct a project network.

$($b$)$ Determine the critical path for this project.

Earliest start and latest completion are shown on the network.

$($c$)$ Construct a Gantt chart to show the activities in time.

$($d$)$ Determine a resource allocation assuming that all activities begin at the earliest possible time.