$2.$ Use Johnson's rule to determine the optimal sequencing for the five jobs to be processed on two machines in a fixed order $($Machine $1$ before Machine $2).$ The processing times are given in the table below.

$($a$)$ What is the optimal sequence?

$($b$)$ What is the total flow time for this sequence?

Job Machine $1$ Machine $2$

L

M

N

$0$

p

$16$

$11$

$18$

$7$

$14$

$9$

$6$

$7$

$10$

$15$