Questions $2$:

$[30]$

You are a project manager overseeing the construction of a new office building. The project involves several activities, each with a specific duration and set of dependencies. The goal is to complete the project in the shortest possible time. Below is the list of activities with their durations and dependencies:

$\backslash$table$[[$Activity$,$Duration $($days$),$Predecessors$],[$A$,5,$None$],[$B$,3,$A$],[$C$,8,$A$],[$D$,6,$B$],[$E$,4,$B$,$ C$],[$F$,2,$C$],[$G$,7,$D$,$ E$],[$H$,3,$E$],[$I$,5,$F$,$ H$],[$J$,6,$H$,$ I$]]$

$2\mathrm{.}1.$ Construct a network diagram.

$(7)$

$2\mathrm{.}2.$ Determine ES$,$ EF$,$ LS$,$ LF$,$ Slack.

$(17)$

$2\mathrm{.}3.$ Determine the critical path and project completion time.

$(3)$

$2\mathrm{.}4.$ If you need to reduce the project duration by $4$ days, identify which activities should be expedited $($crashed$)$ and how many days each should be reduced.

$(3)$