$8$ A manual assembly line must be designed for a product with annual demand of $150,000$ units. The line will operate $50w\frac{k}{y}r,10$ shifts$/$wk$,$ and $7\mathrm{.}5h\frac{r}{s}$hift. Work units will be attached to a continuously moving conveyor. Work content time is $58\mathrm{.}0$min. Assume line efficiency is $0\mathrm{.}95,$ balancing efficiency is $0\mathrm{.}93,$ and repositioning time is $8sec.$ Determine $($a$)$ hourly production rate to meet demand, and $($b$)$ number of workers required.