During the early morning hours, customers arrive at a branch post office at an average rate of $45$ per hour $($Poisson$),$ while clerks can handle transactions in an average time $($exponential$)$ of $4$ minutes each.

If clerk cost is $$30$ per hour and customer waiting time represents a "cost" of $$20$ per hour, how many clerks can be justified on a cost basis?

Select one:

a$.$

$4$

b$.$

$5$

c$.$

$6$

d$.$

$3$