An ERP vendor, $3$DTech is now trying to develop an ERP system for a company. The project manager has identified the critical steps to develop the ERP system. The following network diagram represents the project plan $($numbers in parentheses represent activity durations in weeks$).$ Note that the legend at the top right corner of the network diagram indicates the format used to illustrate earliest start, earliest finish, latest start and latest finish times for each activity.

The marketing manager believes that $3$DTech would have a much higher negotiation power if they can finish the project $2$ weeks earlier. The following table lists activities that can be crashed and the associated costs.

$\backslash$table$[[$Activity$,$Duration$($weeks$),$Crash Cost$/$Week $($$$),$Possible Crash $($weeks$)],[$A$,3,9,000,2],[$B$,2,11,000,1],[$C$,2,7,000,1],[D,7,2,000,3],[E,5,6,000,2],[F,3,9,500,1],[$G$,2,-,-],[H,1,-,-],[1,3,8,000,2],[$J$,6,12,500,3]]$

a$.$ Determine the most economical way to crash the project duration by $2$ weeks. What is the incremental cost incurred in completing this project $2$ weeks earlier?

b$.$ What is $($are$)$ the critical path$($s$)$ after crashing the project by $2$ weeks?