The rocket widget for Guinness is made using a $12-$step process with task names and durations $($in minutes$)$ as shown in the following table. The goal of the line is to produce $40$ rocket widgets in an $8-$hour shift.

Task Duration Predecessors

Task Duration Predecessors

A $5$

G $4$ C

B $8$ A

H $10$ D$,$ G

C $7$ A

I $4$ E

D $12$ B

J $2$ F$,$ H

E $6$ B

K $7$ I

F $8$ C

L $9$ J$,$ K