Problem #$5(20$ points$)$

Six machines will constitute a GT cell. The from$-$to data for the machines are shown in the table below. $($a$)$ Determine the most logical sequence of machines for this data, and construct the network diagram, showing where and how many parts enter and exit the system. $($b$)$ Compute the percentages of in$-$sequence moves, bypassing moves, and backtracking moves in the solution.

$\backslash$table$[[,$To$],[$From$,1,2,3,4,5,6],[1,,43,,,15,31],[2,,,38,36,,21],[3,58,44,,,,],[4,,,,,5,],[5,,,,,,17],[6,,8,,48,,]]$