$(20\text{'})$ Consider $P_4||$ prec $|C_{\text{m}\text{a}\text{x}}|$ with $12$ jobs.

$\backslash$table$[[$jobs$,1,2,3,4,5,6,7,8,9,10,11,12],[p_j,10,10,10,12,11,10,12,12,10,10,10,10]]$

The jobs are subject to the precedence constraints depicted below. PLEASE SPET BY STEP

$($a$)$ Apply the generalized version of the CP rule: every time a machine is freed select the job at the head of the string with the largest total amount of processing. $(5\text{'})$

$($b$)$ Apply the generalized version of the LNS rule: every time a machine is freed select the job that precedes the largest total amount of processing. $(5\text{'})$

$($c$)$ Is either one of these two schedules optimal? $(10\text{'})$