A process is scheduled to run $24$ hours every weekday across $3$ shifts. Each shift gets a $20-$minute break. There is also a $10-$minute production meeting at the start of each shift. The total operation time for $1$ part is $0\mathrm{.}8$ minute.

$($Hint: all times must be converted to seconds first$).$

The demand for the product is $275,000$ parts per week.

a$)$ Determine the TAKT time for the process and explain briefly what this means.

b$)$ Determine the number of workers required in this process.