improve processing and interoffice communications for a particular company. Contained in the proposal is a list of activities that must be achieved to complete the new office system project. The time unit is week.

$\backslash$table$[[$Activity$,\backslash$table$[[$Immediate$],[$Predecessor$]],\backslash$table$[[$Normal$],[$Time$]],\backslash$table$[[$Crash$],[$Time$]],\backslash$table$[[$Normal$],[$Cost$]],\backslash$table$[[$Crash$],[$Cost$]]],[$None$,9,8,7,000,10,000],[$B$,$A$,8,5,9,500,20,000],[$C$,$A$,15,10,10,000,30,000],[$D$,$B$,$ C$,5,3,1,000,5,000],[$E$,$C$,10,9,37,500,40,000],[$F$,$D$,$ E$,2,1,15,000,20,000]]$

$5-43$

Crashing Exercise $1($cont$...)$

$(1)$ Show the critical path$($s$)$ under the normal activity completion times.

$(2)$ To reduce the project completion time by $1$ week, which activities should be crashed?

$(3)$ To shorten the project completion time by $3$ weeks, which activities would be shortened and what would be the final total project costs be$?$ Show, step by step, how you arrive at the schedule.