$($a$)$ Formulate a linear programming model that can be used to make the crashing decisions for this project. $($The objective function should be the additional cost of crashing. Let $x_i=$

the finish time for activity i and $y_i=$ the amount of time activity $i$ is crashed where $i=A,B,C,D,E,F,G,$ and $H.)$

Min

constraint A

constraint B

$C$ depends on

D depends on $C$

$D$ depends on $B$

$E$ depends on $D$

$F$ depends on $E$

$G$ depends on $C$

$G$ depends on $B$

$H$ depends on $G$

finish time for $H$

maximum crashing for $A$

maximum crashing for $B$

maximum crashing for $C$

maximum crashing for $D$

maximum crashing for $E$

maximum crashing for $F$

maximum crashing for $G$

maximum crashing for $H$

$($b$)$ Solve the linear programming model and make the minimum cost crashing decisions. What is the amount of crash time $($in weeks$)$ for each activity?

What is the added cost $($in dollars$)$ of meeting the $16-$week completion time?

$($c$)$ Develop a complete activity schedule based on the crashed activity times.