As part of a major plant renovation project, the industrial engineering department has been asked to balance a revised assembly operation to achieve an output of $240$ units per eight$-$hour day. Task times and precedence relationships are as follows:

Task Duration

$($minutes$)$ Immediate

Predecessor

a $0\mathrm{.}2-$

b $0\mathrm{.}4$ a

c $0\mathrm{.}2$ b

d $0\mathrm{.}4-$

e $1\mathrm{.}2$ d

f $1\mathrm{.}2$ c

g $1\mathrm{.}0$ e$,$ f Determine the minimum number of stations needed