Assume you are working for a company that produces $8$ different types of parts with $7$ machines. Each part has a different route to follow. The machine routes for each part are given in the following table.$$PARTS

P$1$

P$2$

P$3$

P$4$

P$5$

P$6$

P$7$P$8$

ROUTING

M$1-$M$4-$M$7$ M$3-$M$5-$M$1-$M$2$ M$4-$M$7-$M$1-$M$2$ M$3-$M$6-$M$2$ M$3-$M$6-$M$5$ M$1-$M$7-$M$3$ M$1-$M$6-$M$7-$M$4$ M$6-$M$2-$M$5$Considering the routes for each part, find out part families and group the machines into cells.