Office Automation Inc., developed a proposal for implementing a software system that will standardize the accounts payable function by automatically issuing an electronic payment upon receipt of the vendor invoice. Contained in the proposal is a list of activities that must be accomplished to complete the project. The following table contains relevant information about the activities.

$\backslash$table$[[,$Time $($weeks$),$Cost $($$$1,000$s$),],[$Activity$,$Description,$\backslash$table$[[$Immediate$],[$Predecessor$]],$Normal,Crash,Normal,Crash$],[$A$,$Plan needs,,$10,8,30,70],[$B$,$Order equipment,A$,8,6,120,150],[$C$,$Install equipment,B$,10,7,100,160],[$D$,$Set up training lab,A$,7,6,40,50],[$E$,$Conduct training course,D$,10,8,50,75],[$F$,$Test system,C$,$ E$,3,3,60,]]$

$($a$)$ Develop a project network.

$($b$)$ Develop an activity schedule.

$\backslash$table$[[$Activity$,\backslash$table$[[$Earliest$],[$Start$]],\backslash$table$[[$Latest$],[$Start$]],\backslash$table$[[$Earliest$],[$Finish$]],\backslash$table$[[$Latest$],[$Finish$]],$Slack$],[$A$,0,0,10,10,0],[$B$,10,10,18,18,0],[$C$,18,18,28,28,0],[$D$,10,10,18,18,1],[$E$,17,17,28,28,1],[$F$,,28,31,,]]$

$($c$)$ What are the critical activities? $($Enter your answers as a comma$-$separated list.$)$

$A,B,C,E,F$

What is the expected project completion time $($in weeks$)?$

weeks

$($d$)$ Assume that the company wants to complete the project in six months or $26$ weeks. What is the amount of crash time $($in weeks$)$ for each activity that minimizes cost?

$(A,B,C,D,E)=(,)$

$($e$)$ Develop an activity schedule for the crashed project.

$\backslash$table$[[$Activity$,\backslash$table$[[$Earliest$],[$Start$]],\backslash$table$[[$Latest$],[$Start$]],\backslash$table$[[$Earliest$],[$Finish$]],\backslash$table$[[$Latest$],[$Finish$]],$Slack$],[$A$,,8,8,0,],[$B$,,8,14,14,0],[$C$,14,14,23,23,0],[$D$,,8,14,14,0],[$E$,,14,23,23,0],[$F$,,22,,,]]$

$($f$)$ What added project cost $($in thousands of dollars$)$ is required to meet the six$-$month completion time?

thousands of dollars