$2\mathrm{.}2.$ Consider the instance of $1||L_{\text{m}\text{a}\text{x}}$ with the following processing times and

due dates.

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

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

wards 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 $d_j+p_j$;

$($ii$)$ sequence the jobs in increasing order of $d_j{p}_j$;

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

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