Question $3.(30$ points$)$

ABC computer Co$.$ Ltd$.$ is designing an assembly line to produce $196$ keyboards per an $8$ hr shift. The following table identifies the work elements, times, and immediate predecessors.

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

$\backslash$hline Task & Task time $($sec$)$ & Preceding tasks $\backslash \backslash$

$\backslash$hline A & $40$ & None $\backslash \backslash$

$\backslash$hline B & $80$ & A $\backslash \backslash$

$\backslash$hline C & $30$ & D$,$ E$,$ F $\backslash \backslash$

$\backslash$hline D & $120$ & B $\backslash \backslash$

$\backslash$hline E & $15$ & B $\backslash \backslash$

$\backslash$hline F & $20$ & B $\backslash \backslash$

$\backslash$hline G & $25$ & A $\backslash \backslash$

$\backslash$hline H & $145$ & G $\backslash \backslash$

$\backslash$hline I & $130$ & H $\backslash \backslash$

$\backslash$hline J & $115$ & C$,$ I $\backslash \backslash$

$\backslash$hline

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

$1)$ Find an optimum layout in the sequence of workstations where every work element is assigned in a workstation. Provide the sequence of workstations by indicating WS$1,$ WS$2,$ WS$3....,$ with tasks clearly. $(20$ points$)$

$1)$ Find efficiency of the optimum layout. $(10$ points$)$