$2\mathrm{.}2.$ Consider the instance of $1||$ Lmax with the following processing times and

due dates.

jobs $1234$

pj $5436$

dj $351112$

$($a$)$ Find the optimal sequence and compute the value of the objective.

$($b$)$ Give an argument for positioning jobs with earlier due dates more towards

the beginning of the sequence and jobs with later due dates more

towards the end of the sequence.

$($c$)$ Give an argument for positioning jobs with smaller processing time

more towards the beginning of the sequence and jobs with larger processing

time more towards the end of the sequence.

$($d$)$ Determine which one of the following four rules is the most suitable

generic rule for the problem:

$($i$)$ sequence the jobs in increasing order of dj $+$ pj ;

$($ii$)$ sequence the jobs in increasing order of djpj ;

$($iii$)$ sequence the jobs in increasing order of dj ;

$($iv$)$ sequence the jobs in increasing order of pj $.$