A new order filling system needs to be installed as soon as possible. The table on the next page lists that project$$s activities and their predecessors. Also provided is the cost information to reduce the standard activity times. $($problem $7-32$ in the textbook$)$

$($a$)$ Construct a project network for this problem. Determine the EST, EFT, LST$,$ LFT$,$ and slack for each activity. Also determine the critical path and project completion time.

$($b$)$ Set up and solve an LP model using Excel to crash this project to $24$ days. What is the total crashing cost? $*$PLEASE INCLUDE EXCEL WITH LP SET UP$*\backslash$table$[[$ACTIVITY$,\backslash$table$[[$IMMEDIATE$],[$PREDECESSORS$]],\backslash$table$[[$STANDARD$],[$TIME $($Days$)]],\backslash$table$[[$STANDARD$],[$COST$]],\backslash$table$[[$CRASH TIME$],[($Days$)]],$CRASH COST$],[$A$,--,7,$$$2,000,5,$$$3,500],[$B$,$A$,10,$$$3,000,8,$$$4,700],[$C$,$A$,8,$$$3,400,7,$$$3,700],[$D$,$C$,6,$$$1,600,4,$$$2,600],[$E$,$C$,7,$$$1,900,4,$$$4,000],[$F$,$D$,$E$,5,$$$1,200,3,$$$2,800],[$G$,$B$,$C$,11,$$$8,200,8,$$$10,900],[$H$,$F$,$G$,4,$$$2,600,3,$$$3,800]]$