$3\mathrm{.}9($A$)$ A mass$-$production plant has eight machines and currently operates one $8-$hr shift$/$day$,5$ days$/$wk$,50$ wk$/$yr$.$ Each machine produces the same part at a rate of $24$ parts$/$hr$.($a$)$ Determine the annual production capacity of this plant. $($b$)$ If the plant were to operate three $8-$hr shifts$/$day$,7$ days$/$wk$,52w\frac{k}{y}r,$ then what is the annual percentage increase in plant capacity?