Consider a production situation in which we have multiple identical machines in one work station. The time to load parts to this machine is $2$ minutes, and the time to unload is $1$ minute. It takes approximately $5$ minutes to perform a quality inspection and walk to another machine. The machine takes approximately $50$ minutes to perform the process on the units.

a$)(3$ points$)$ What is the ideal number of machines for one worker?

b$)[5$ points$]$ How many machines should be assigned to worker such that there is no idle time for the machine? What is the correspondine expected repeated cvcle time?