Question $6(6$ marks$)$

A manufacturing company needs to schedule $5$ jobs on two machines. The processing times for each job on both machines are given in the table below.

$\backslash$begin$\{$tabular$\}\{|$c$|$c$|$c$|\}$

$\backslash$hline Job & Machine $1($P$1)($hrs$)$ & Machine $2($P$2)($hrs$)\backslash \backslash$

$\backslash$hline A & $4$ & $6\backslash \backslash$

$\backslash$hline B & $5$ & $3\backslash \backslash$

$\backslash$hline C & $2$ & $8\backslash \backslash$

$\backslash$hline D & $3$ & $7\backslash \backslash$

$\backslash$hline E & $6$ & $4\backslash \backslash$

$\backslash$hline

$\backslash$end$\{$tabular$\}$

a$)$ Determine the optimal job sequence using Johnson's Rule.

b$)$ Calculate the total makespan $($the total time to complete all jobs$)$ based on the optimal sequence.