Problem $3$: An Assembly Line Balancing Problem

A Shop works a $400-$minute day. The manager of the shop wants an output of $200$ units per day for the assembly line that has the elemental tasks shown in the table.

Task. Immediate successor. Task$-$time.

a b$,$ c$,$ d $0\mathrm{.}5$

b e $1\mathrm{.}4$

c e $1\mathrm{.}2$

d f $0\mathrm{.}7$

e g$,$ j $0\mathrm{.}5$

f i $1\mathrm{.}0$

g h $0\mathrm{.}4$

h k $0\mathrm{.}3$

i j $0\mathrm{.}5$

j k $0\mathrm{.}8$

k m $0\mathrm{.}9$

m end. $0\mathrm{.}3$

Please:

$1.$ Construct the precedence diagram.

$2.$ Assign tasks using the most$-$following$-$tasks rule as the primary rule and the greatest$-$positional$-$weight rule as the secondary rule.

$3.$ Compute the balance delay and the efficiency of your balance.