A clothing manufacturer is upgrading their production machinery. The company operates three eight$-$hour shifts per day; they would like to minimize down$-$time during the upgrade.

$\backslash$table$[[,$Activity,Precedes,$\backslash$table$[[$Duration$],[($hours$)]]],[$A$,$Order and receive new machines P and Q$,$B$,480],[$B$,$Stop production,C$,$ G$,$ H$,2],[$C$,$Remove old machine Q$,$D$,2],[$D$,$Prepare machine base for Q$,$E$,8],[$E$,$Install new machine Q$,$F$,2],[$F$,$Test and commission machine Q$,$L$,3],[$G$,$Remove old machine P$,$H$,1],[$H$,$Prepare new electrical feed for P$,$J$,$ L$,5],[$J$,$Install new machine P$,$K$,2],[$K$,$Commission and test machine P$,$L$,12],[$L$,$Start production,,$1]]$

a$.$ How much production down$-$time is needed for this project?

b$.$ Using your knowledge of production systems, revise the project precedence to minimize the production down$-$time. Justify your answer.