Alcoa Inc. has analyzed the setup time on its computer$-$controlled lathe. The setup requires changing the type of fixture that holds a part. The average setup time has been $140$ minutes, consisting of the following steps:

$\backslash$table$[[$Step$,$Time $($in minutes$)],[$Turn off machine and remove fixture from lathe,$13],[$Go to tool room with fixture,$15],[$Record replacement of fixture to tool room,$18],[$Return to lathe,$21],[$Clean lathe,$17],[$Return to tool room,$21],[$Record withdrawal of new fixture from tool room,$12],[$Return to lathe,$15],[$Install new fixture and turn on machine,$8],[$Total setup time,$139]]$