Question $1$:

A manual assembly line is being planned to produce a small consumer appliance. The work elements, element times, and precedence constraints are indicated in the table below. The workers will work for $\backslash (420\backslash$mathrm$\{$~min$\}/\backslash$mathrm$\{$shift$\}\backslash )$ and must produce $381$ units$/$day$.($a$)$ Use the largest candidate rule to solve the line balancing problem. $($b$)$ For your line balancing solution, compute the balancing efficiency. $($c$)$ Solve using ranked positional weighted method and recalculate balancing efficiency.

$\backslash$begin$\{$tabular$\}\{$ccc$|$ccc$\}$

$\backslash$hline $\backslash$begin$\{$tabular$\}\{$c$\}$

Work $\backslash \backslash$

element

$\backslash$end$\{$tabular$\}$ & $\backslash (\backslash$mathrm$\{$T$\}\_\{\backslash$mathrm$\{$e$\}\}(\backslash$mathrm$\{$min$\})\backslash )$ & $\backslash$begin$\{$tabular$\}\{$c$\}$

Immediate $\backslash \backslash$

predecessors

$\backslash$end$\{$tabular$\}$ & $\backslash$begin$\{$tabular$\}\{$c$\}$

Work $\backslash \backslash$

element

$\backslash$end$\{$tabular$\}$ & $\backslash (\backslash$mathrm$\{$T$\}\_\{\backslash$mathrm$\{$e$\}\}(\backslash$min $)\backslash )$ & $\backslash$begin$\{$tabular$\}\{$c$\}$

Immediate $\backslash \backslash$

predecessors

$\backslash$end$\{$tabular$\}\backslash \backslash$

$\backslash$hline $1$ & $0\mathrm{.}4$ & $-$ & $8$ & $0\mathrm{.}15$ & $4\backslash \backslash$

$2$ & $0\mathrm{.}5$ & $1$ & $9$ & $0\mathrm{.}41$ & $5\backslash \backslash$

$3$ & $0\mathrm{.}2$ & $1$ & $10$ & $0\mathrm{.}2$ & $6,7\backslash \backslash$

$4$ & $0\mathrm{.}6$ & $-$ & $11$ & $0\mathrm{.}3$ & $8\backslash \backslash$

$5$ & $0\mathrm{.}25$ & $2$ & $12$ & $0\mathrm{.}33$ & $9,10\backslash \backslash$

$6$ & $0\mathrm{.}3$ & $3$ & $13$ & $0\mathrm{.}4$ & $11\backslash \backslash$

$7$ & $0\mathrm{.}37$ & $4$ & $14$ & $0\mathrm{.}62$ & $12,13\backslash \backslash$

$\backslash$hline

$\backslash$end$\{$tabular$\}$