$(25\%)$ Based on the flow data from the From$-$To chart and an initial layout given below $($assume all departments are the same size $-{10}^{\text{'}}{10}^{\text{'}}),$ manually apply $($showing all steps$)$ the $2-$opt$/$CRAFT$/$SDPIM algorithm to find a solution $($use a sequence of $1-2-3-4$ as the initial layout as shown in the diagram below$).$ Compare your solution to the lower bound for the problem.

From$-$To Chart

$\backslash$table$[[,$Rec,Fab,Asn,Test$],[$Rec$,-,120,240,10],[$Fab$,0,-,5,20],[$Asm$,0,250,-,30],[$Test$,5,20,15,-]]$

Initial Layout

$\backslash$table$[[$Rec$,$Fab$],[$Asm$,$Test$]]$