One$/$half million parts of a certain type are to be manufactured annually on dedicated production machines that run $16$ hours per day, five days per week, $50$ weeks per year. $($a$)$ The cycle time to produce one part is $1\mathrm{.}8$min. If availability and utilization are each $100\%,$ and setup time is neglected, how many of the machines will be required to satisfy demand? $($b$)$ Solve part $($a$)$ except that availability $=95\%.$