Next consider the $2$Xfaster$$ machine. As its name suggests, $2$Xfaster can work twice as fast as the Classic machine, i$.$e$.,$ it can serve, on average, $40$ customers per hour, although it only processes one drink order at a time. The service time for $2$Xfaster is also exponentially distributed. A $2$Xfaster machine is significantly larger than the Coffee Classic, so the physical limitations of the store would only allow for the purchase of one machine.

$13.$ What is the utilization of the $2$Xfaster machine? Please enter your answer as a value between $0$ and $1.$ If your answer is not an integer, provide at least three decimal places, e$.$g$.,7\mathrm{.}500.$

$14.$ With the $2$Xfaster machine, what is the expected total time $($in minutes$)$ that a customer spends in the store $($i$.$e$.,$ the total time in queue and in service$)?$ If your answer is not an integer, provide at least three decimal places, e$.$g$.,7\mathrm{.}500.$

$15.$ With the $2$Xfaster machine, what is the expected total number of customers in the store $($i$.$e$.,$ in queue and in service$)?$ If your answer is not an integer, provide at least three decimal places, e$.$g$.,7\mathrm{.}500.$

Hint: Please ensure that all quantities are in the same units!

$16.$ Management is worried about the cost of excessive customer waiting time, because each moment that customers wait increases the chance of customer abandonment and balking. After some analysis, the manager estimates that the hourly cost to the coffee shop for a customer$$s total time spent in the store is $$10($that is$,$ the waiting cost rate is $$10$ per customer per hour, which accounts for time in the queue and time being served$).$ If you estimate that a customer spends on average W minutes in the store $($in queue $+$ being served$),$ what is the average total

waiting cost per hour?

a$.$ $$10\backslash$times $($W$/60)$

b$.$ $$10\backslash$times $32\backslash$times $($W$/60)$

c$.$ $$10\backslash$times $40\backslash$times $($W$/60)$

d$.$ $$10\backslash$times $(32/40)\backslash$times $($W$/60)$