Question $1$: Assume you are working for a company that produces six different types of parts with seven machines. Each part has a different route to follow. The machine routes for each part are given in the following table.

$\backslash$table$[[$PARTS$,$ROUTING$],[$P$1,$M$4-$M$1-$M$7],[$P$2,$M$2-$M$6-$M$3-$M$4],[$P$3,$M$5-$M$1-$M$4-$M$7],[$P$4,$M$5-$M$2-$M$4],[$P$5,$M$2-$M$3-$M$6],[$P$6,$M$4-$M$1-$M$6]]$