$[15$ points$]$ A forensic analysis lab received eight forensic analysis jobs. The processing time for each job and the expected due date for each job are as follows:

$\backslash$table$[[$Job$,1,2,3,4,5,6,7,8],[$Processing Time $($minutes$),70,75,100,45,55,90,60,55],[\backslash$table$[[$Due Date $($minutes from$],[$the start time$)]],180,350,120,420,200,360,90,450]]$

a$.$ Assume that all jobs are available to start at time $0.$ Calculate and compare the average flowtime, lateness, and tardiness for the following sequencing rules:

i$.$ Process in the order they have arrived $($First come first serve$)$

ii$.$ Shortest processing time

iii. Earliest due date

b$.$ If you want to minimize the largest lateness$/$tardiness$,$ which sequencing rule is best? Explain using the results in $($a$).$