Formulate a linear programming model that can be used to assist with the crashing decisions. $($The objective function should be the additional cost of crashing. Let

xi $=$

the finish time for activity i and

yi $=$

the amount of time activity i is crashed where i $=$ A$,$ B$,$ C$,$ D$,$ E$,$ F$,$ and G$.$ Let

xFIN $=$

the finish time for the entire project.$)$

Min

s$.$t$.$

constraint A

constraint B

C depends on A

D depends on B

E depends on D

E depends on C

F depends on D

F depends on C

G depends on F

project finish time depends on E

project finish time depends on G

maximum project finish time

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

All x$,$ y $>=0$