$1$ Four parts $($A$,$ B$,$ C$,$ and D$)$ are processed through a sequence of four operations $,$ and $4).$ Not all parts are processed in all operations. Part A$,$ which has weekly quantities of $70$ units, is processed through operations $1,2,$ and $3$ in that order. Part B$,$ which has weekly quantities of $90$ units, is processed through operations $2,4,$ and $1$ in that order. Part C$,$ which has weekly quantities of $65$ units, is processed through operations $3,2,$ and $4$ in that order. Finally, part D$,$ which has weekly quantities of $100$ units, is processed through operations $2,1,$ and $4$ in that order. $($a$)$ Draw the network diagram and $($b$)$ prepare the From$-$To table for this work system.