$($a$)$ A particular operation uses a two$-$step sequence that all jobs in a certain category follow. For the group of jobs listed below;

Processing time $($minutes$)$

Jobs a b c d e

Workstation A $2718702615$

Workstation B $4533302410$

$($i$)$ Find the sequence that will minimise the total completion time. $(4$ marks$)$

$($ii$)$ Construct a progress chart for the sequence of jobs. Clearly identify the amount of idle time at workstation B and the makespan of the batch of jobs. $(5$ marks$)$

$($iii$)$ What jobs are candidate for splitting? Why? If they were split, how much would idle time and makespan time be reduced? $($Assume splitting the jobs in half$)$