$(4-$a$)$ The company FlexIt Inc. wants to buy two new machines. These can either both be of type A or both be of type B$.$ Buying a mixture of the two types is not possible. The machines are meant to process items that arrive with an expected arrival rate of $\backslash (\backslash$lambda$=9\mathrm{.}2\backslash )$ items per minute and that wait for their service in a single queue. Since the space is costly$,$ FlexIt Inc. wants to select the machine type with the lower expected queue length. The parameters of the two alternatives are given in the table below. Unfortunately, the coefficient of variation of the service times for machine type A is not known, but the expected queue length $\backslash (\backslash$mathrm$\{$E$\}\backslash$left$[$L$\_\{$q$\}\backslash$right$]\backslash )$ of machine type A is observed from another manufacturing plant. Calculate the expected queue length $\backslash (\backslash$mathrm$\{$E$\}\backslash$left$[$L$\_\{$q$\}\backslash$right$]\backslash )$ for machine type B and make a suggestion of which machine type FlexIt Inc. should choose. Additionally, calculate for both machine types the expected cycle time $\backslash (\backslash$mathrm$\{$E$\}\backslash$left$[$W$\_\{$s$\}\backslash$right$]\backslash ).$

$(8$ Points$)$