Five jobs are required to be completed in a two$-$machine flow shop and their respective needed times are

shown in the next table. Each job must begin with machine A and finish with machine B$.$

Time $($minutes$)$

Job Machine A Machine B

$156$

$234$

$369$

$478$

$592$

a$.$ Determine the sequence that will minimize the make$-$span.

b$.$ Construct a load Gantt chart for the resulting sequence and find machine A$$s idle time.

c$.$ For the sequence determined in part a$,$ can machine A$$s idle time be reduced by splitting some jobs

in half? If so$,$ which jobs?

d$.$ Split jobs $3$ and $5$ and draw the new load Gantt chart.