I$-$mart is a discount optical shop that can fill most prescription orders in around one hour. The management is analyzing the processes at the store. There currently is one person assigned to each task below. The optometrist assigned to task $$B$$ takes an hour off for lunch and the other employees work the entire day.

TASK TIME

A$.$ Greet$/$register the patient $3$ minutes$/$patient

B$.$ Optometrist conducts eye exam $20$ minutes$/$patient

C$.$ Frame$/$lenses selection $21$ minutes$/$patient

D$.$ Glasses made $($process can run $6$ pairs of glasses at the same time$)66$ minutes$/$patient

E$.$ Final fitting $6$ minutes$/$patient

For a typical $10-$hour retail day $(10$ A$.$M$.-8$ P$.$M$.),$ the manager would like to calculate the following:

a$.$ Assuming every patient requires glasses, what is the current maximum output of the process per day? $($assume an hour break for