You have collected the data for a process. The activity time is given below.

Activity, Immediate Predecessors, Activity time $($Days$),$ Possible Crash Time $($Days$),$ Crash Cost Per Day

A$,$ None, $2,2,$ $$1,000$

B$,$ A$,3,1,$ $$200$

C$,$ B$,4,0$

D$,$ B$,3,3,$ $$100$

E$,$ C and D$,3,2,$ $$500$

F$,$ E$,5,1,$ $$900$

$($a$)$ Construct a flow chart based on the information in the table. For each activity, report the earliest start, earliest finish, latest start, latest finish times, and the slack time on the diagram using Forward pass and Backward pass. Report the process flow time $($i$.$e$.,$ project completion time$)$ and critical path$($s$).$

$($b$)$ According to the flow chart you draw in $($a$),$ if Activity B is delayed by $1$ day, then what will happen to the process flow time $($increase$,$ decrease or unchanged$)?$

$($c$)$ You want to reduce $($or shorten$)$ the process flow time by $1$ day, which activity should be crashed to minimize the cost?