The times required to complete each of five jobs in a two$-$machine flow shop are shown in the following table. Each job must begin with machine A$,$ and end with machine B$.$

Time $($hours$)$

Job Machine A Machine B

a $65$

b $43$

c $96$

d $87$

e $29$

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

multiple choice $1$

e$-$d$-$c$-$a$-$b

b$-$c$-$a$-$e$-$d

d$-$a$-$b$-$c$-$e

a$-$b$-$c$-$d$-$e

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

Idle time for machine B

hours

c$.$ For the sequence determined in part a$,$ can machine B$$s idle time be reduced by splitting some jobs in half? If so$,$ which jobs?

$($Click to select$)($yes $/$ no$),$ split $($Click to select$)($both c and b $/$ both c and a $/$ none$).$