Four workstations $,$ and $4)$ are used to produce similar parts. The stations are to be arranged into a work cell with an in$-$line layout. The daily flow of parts between workstations is as follows: $15$ parts from stations $2$ to $4,60$ parts from stations $3$ to $2,35$ parts from stations $2$ to $1,20$ parts from stations $4$ to $3,$ and $30$ parts from stations $4$ to $2.($a$)$ Use the Hollier algorithm to determine the most logical sequence of stations in the work system. $($b$)$ Draw the network diagram for the system. $($c$)$ Compute the percentage of in$-$sequence moves, by$-$passing moves, and backflow moves for the sequence.