Kimpel Products makes pizza ovens for commercial use. James Kimpel, CEO, is contemplating producing smaller ovens for use in high school and college kitchens. The activities necessary to build an experimental model and related data are listed in the following table:

$\backslash$table$[[,\backslash$table$[[$Normal$],[$Activity$]],\backslash$table$[[$Crash$],[$Time $($weeks$)]],\backslash$table$[[$Normal$],[$Cost$]],\backslash$table$[[$Total Cost$],[$with$],[$Crashing$]],$Immediate Predecessor$($s$)],[$A$,3,2,$$$1,400,$$$2,100,-],[$B$,2,1,$$$2,100,$$$2,850,-],[$C$,1,1,$$$300,$$$300,-],[$D$,7,3,$$$1,500,$$$1,800,$A$],[$E$,6,3,$$$950,$$$1,250,$B$],[$F$,2,1,$$$4,000,$$$5,200,$C$],[$G$,4,2,$$$1,500,$$$2,200,$D$,$ E$]]$

a$)$ Based on the given information regarding the activities for the project, the project completion date $=14$ weeks.

b$)$ To reduce the duration of the project to $10$ weeks at the least cost, the following is the order of what needs to be followed while crashing the activities:

The first activity to crash is by $2$ weeks at a per week crashing cost of $75$ dollars.

Next, one should crash activity $D$ and activity of dollars. by $2$ weeks for an additional total per week crashing cost