This section is similar to your practice exam $($as any good test should be$).$ In the early $20$th century, the Danish mathematician and engineer Agner Erlang developed queuing theory to find out how many telephone operators were needed to process a given volume of calls$---$so a customer was not $"$on hold" $($or in a telephone queue$)$ for too long. Suppose that data for Erlang's company showed that, on average, $=144$ calls per hour need to be handled $($with the exponential distribution as a reasonable picture of interarrival times$).$ The time needed to help a customer $($service or processing time$)$ is exponentially distributed with a mean of E$[$T$]=6$ minutes.

What is the capacity of an individual operator, $($in customers per hour$)?$

a$.8$ customers per hour

b$.10$ customers per hour

c$.6$ customers per hour

d$.12$ customers per hour

Clear my choice

Assist Erlang in calculating how many operators $"$s$"$ are needed such that the mean waiting time is less than three minutes. We know that a waiting time of $E[W_q]<mn\; id="EditorElement\_1434223">1</mn><mn\; id="EditorElement\_1434224">0</mn>$ minutes corresponds to a utilization of $=0\mathrm{.}96.$

a$.9$ operators

b$.12$ operators

C$.18$ operators

d$.15$ operators