QUESTION $2(24$ marks$)$

$($a$)$ A construction project involves the activities listed in Table $2\mathrm{.}1.$ Information on the immediately preceding activity $($IPA$),$ normal duration and cost, as well as crash duration and cost for each activity are also provided in the table. The indirect cost for the project is $$4M$ per month.

$($i$)(4$ marks$)$ Draw the activity$-$on$-$arrow network diagram for this project; identify the critical path and project duration based on normal activity durations.

$($ii$)(12$ marks$)$ If the project team wants to shorten the project duration by $2$ months with the least increase in direct costs, what is the total project cost and critical path as a result of the shortening?

Table $2\mathrm{.}1$ List of activities for project in Question $2($a$)$

$\backslash$table$[[$Activity$,$IPA,$\backslash$table$[[$Normal Duration$],[($months$)]],\backslash$table$[[$Normal$],[$Direct Cost$]],\backslash$table$[[$Crash Duration$],[($months$)]],\backslash$table$[[$Crash$],[$Direct Cost$]]],[$A$,-,5,$$$6M,5,$$$6M$