$5.$ Consider two different machines A and B that could be used at a station. Machine A has a mean effective process time te of $1\mathrm{.}0$ hours and an SCV ce$2$ of $0\mathrm{.}25.$ Machine B has a mean effective process time of $0\mathrm{.}85$ hour and an SCV of $4.($Hint: You may find a simple spreadsheet helpful in making the calculations required to answer the following questions.$)$

$($a$)$ For an arrival rate of $0\mathrm{.}92$ job per hour with c$2$a $=1,$ which machine will have a shorter average cycle time?

$($b$)$ Now put two machines of type A at the station and double the arrival rate $($i$.$e$.,$ double the capacity and the throughput$).$ What happens to cycle time? Do the same for machine B$.$ Which type of machine produces shorter average cycle time?

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$($c$)$ With only one machine at each station, let the arrival rate be $0\mathrm{.}95$ job per hour with c$2$ a $=1.$ Recompute the average time spent at the stations for both machine A and machine B$.$ Compare with $($a$).$

$($d$)$ Consider the station with one machine of type A$.$

i$.$ Let the arrival rate be $12$ job per hour. What is the average time spent at the station?

What happens to the average time spent at the station if the arrival rate is increased by $1$ percent $($i$.$e$.,$ to $0\mathrm{.}505)?$ What percentage increase in wait time does this represent?

ii$.$ Let the arrival rate be $0\mathrm{.}95$ job per hour. What is the average time spent at the station? What happens to the average time spent at the station if the arrival rate is increased by $1$ percent $($i$.$e$.,$ to $0\mathrm{.}9595)?$ What percentage increase in wait time does this represent?