Further to the data provided above for $3$ estimates, the management is now contemplating crashing the network to the minimum possible time under the crash cost schedule provided below. $($a$)$ What would be the minimum duration of the project? and $($b$)$ what is the corresponding crash cost? $($c$)$ If the management wishes to crash the project down to $29\mathrm{.}85$ weeks only, what will be the total cost incurred and corresponding crash schedule? You must submit computer outputs $($original$)$ for questions #$5$ and #$6$ to earn credits.

Activity $$ Normal Time in weeks$*$ Crash time in weeks Normal Cost $($$$)**$ Crash Cost $($$$)**$ A $7\mathrm{.}11761000011500$

B $3\mathrm{.}05280009000$

C $2\mathrm{.}51500016000$

D $472507895$ E $5\mathrm{.}5750010000$ F $3\mathrm{.}580009000$ G $1\mathrm{.}9510001250$ H $3\mathrm{.}555005800$ I $31000015000$ J $820005000$ K $0\mathrm{.}170008000$ L $0\mathrm{.}580009000$ M $7\mathrm{.}560009000$ N $5\mathrm{.}550007000$ O $560008000$ P $1860009000$ Q $3\mathrm{.}580009000$ R $2\mathrm{.}560008000$ S $2\mathrm{.}5900010000$ T $380008200$ U $570008000$ V $650005600$ W $3\mathrm{.}580009500$ X $71000015000$ Y $5\mathrm{.}5500010000$ Z $5\mathrm{.}560008000$

$*$Populate this column from your calculation from question #$5.$ For example the entry corresponding to activity A $=($a $+4$m $+$ b$)/6=(5\mathrm{.}6+(4$ x $7)+9\mathrm{.}1)/6=7\mathrm{.}117$ weeks $($Rounded to three decimal points$)$; Activity B similarly is $3\mathrm{.}05$ weeks.