Problem $3.(40$ points$)$

The Pohl Pool Company has seven jobs waiting to be processed through its liner department. Each job's estimated processing times and due dates are as follows:

$\backslash$begin$\{$tabular$\}\{|$c$|$c$|$c$|\}$

$\backslash$hline Job & Processing Time $($Days$)$ & Due Date $($Days from Now$)\backslash \backslash$

$\backslash$hline A & $4$ & $8\backslash \backslash$

$\backslash$hline B & $13$ & $37\backslash \backslash$

$\backslash$hline C & $6$ & $8\backslash \backslash$

$\backslash$hline D & $3$ & $7\backslash \backslash$

$\backslash$hline E & $11$ & $39\backslash \backslash$

$\backslash$hline F & $9$ & $21\backslash \backslash$

$\backslash$hline G & $8$ & $16\backslash \backslash$

$\backslash$hline

$\backslash$end$\{$tabular$\}$

a$.$ Using the shortest processing time scheduling rule, in what order would the jobs be completed? Processing can start immediately.

b$.$ What is the average completion time $($in days$)$ of the sequence calculated in part a$?$

c$.$ What is the average job lateness $($in days$)$ of the sequence calculated in part a$?$