Consider two different machines A and $B$ that could be used at a station. Machine A has a mean effective process time $t_e$ of $1\mathrm{.}0$ hours and an SCV $c_e^2$ of $0\mathrm{.}25.$ Machine B has a mean effective process time of $0\mathrm{.}85$ hour and an SCV of $4.$

$($a$)(10pts)$ For an arrival rate of $0\mathrm{.}92$ job per hour with $c_a^2=1,$ which machine will have a shorter average cycle time?

$($b$)(10$ pts $)$ Now put two machines of type A at the station and docule the arrival rate $($i$.$e$.,$ double the capacity and the throughput$).$ What happens to cycle time? Do the same for machine B$.$ Which trype of machine produces shorter average cycle time?

$($c$)(10pts)$ Consider the station with one machine of type A$.$

i$.$ Let the arrival rate be $0\mathrm{.}5$ 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 one percent $($i$.$e$.,$ to $0\mathrm{.}9595)?$ What percentage increase in wait time does this represent?