$15\mathrm{.}1($A$)$ Annual demand for a new assembled product is expected to be $75,000$ units. Work

content time for the product is $25\mathrm{.}8$min. The assembly line works $50w\frac{k}{y}r,40h\frac{r}{w}k.$

Expected line efficiency is $95\%.$ With one worker per station, determine $($a$)$ average hourly

production rate, $($b$)$ cycle time, and $($c$)$ ideal minimum number of workers.