b$)$ Jobs A$,$ B$,$ C$,$ D$,$ E$,$ F and G must go through process I and II in that sequence $($process I first then process II$).$ Use Johnson$$s rule to determine the optimal sequence in which to schedule the jobs to minimize the total required time. How much total time is required to process all the seven jobs? Illustrate this using a Gantt chart.

Job Processing time in I Processing time in II

A $34$

B $1513$

C $76$

D $1112$

E $28$

F $85$

G $74$

$(8$ marks$)$