Coleman Rich Control Devices, Inc, produces custom$-$built relay devices for auto makers. The most recent project undertaken by Rich requires $14$ different activities. Rich's managers would like to determine the total project completion time $($in days$)$ and those activities that lie along the critical path. The appropriate data are shown in the following table:

$\backslash$table$[[$Activity$,$Time $($days$),\backslash$table$[[$Immediate$],[$Predecessor$($s$)]],$Activity,Time $($days$),\backslash$table$[[$Immediate$],[$Predecessor$($s$)]]],[a,m,b,a,m,b$