$2.$ Johnson Cogs wants to set up a line to produce $60$ units per hour. The work elements and their precedence relationships are shown in the following table.

Work Element TIME

$($sec$)$ Immediate

predecessor

A $40$ None

B $30$ A

C $50$ A

D $40$ B

E $6$ B

F $25$ C

G $15$ C

H $20$ D$,$ E

I $18$ F$,$ G

J $30$ H$,$ I

$274$