The DMV currently has two offices located in Bluebell County. Office A is larger and servers the county seat with $6$ officers on duty at any time. At Office A customers arrive every $2\mathrm{.}1$ minutes with a standard deviation of $2\mathrm{.}1$ minutes. Office B is located in a less populous town in the county and has only one officer on duty at any given time. At Office B customers arrive early $14\mathrm{.}1$ minutes with a standard deviation of $14\mathrm{.}1$ minutes. Each arriving customer works with one officer to complete their request and the average processing time is $11$ minutes with standard deviation of $12$ minutes at both locations.

Enter all time calculations in minutes rounded to one decimal place $($the nearest $0\mathrm{.}1$ minutes$).$ Enter utilization as a percentage rounded to the nearest tenth of a percent.

a$.$ Calculate the utilization and average wait time at Office A$.$

Utilization $=$

$\%$

Average wait$-$time $=$

minutes

b$.$ Calculate the utilization and average wait time at Office B$.$

Utilization $=$

$\%$

Average wait$-$time $=$

minutes

c$.$ Recently the DMV has received complaints about long wait$-$times. They are considering closing Office B to pool all the on$-$duty officers in one location. While pooling the resources should reduce the wait times, it will mean that travel times for customers currently served by Office B increase by $20$ minutes round trip on average.

Calculate the new average wait time at Office A$.$ Assume that the arrival rates for the two offices can be added to find the combined arrival rate $($which is not the same as the interarrival time$).$ and that the coefficient of variation for arrivals remains to be $1.$

Utilization $=$

$\%$

Average wait$-$time $=$

minutes

Is the reduction in wait$-$time due to combining the two offices enough to justify the additional driving time for customers previously served by Office B$?$ Will the average wait time for customers previously served at Office A increase as a result of combining the two offices?

Enter the decrease in total average wait time for customers previously served by Office A $($enter $0$ if wait times have increased for those customers$).$

minutes.

Enter the decrease in total average time $($wait time $+$ travel time$)$ for customers previously served by Office B $($enter $0$ if total time has increased for those customers$)$:

minutes.