An I.T$.$ team repairs computers that break down at an average of $=2\mathrm{.}5$ per hour $($approximately Poisson in nature$).$ The team can service an average of $2$ computers every $30$ minutes with a repair time distribution that approximates an exponential distribution. The department is open $10$ hours per day. The team$$s approximate cost $$125$ per hour. The cost associated with lost productivity from the breakdown is estimated at $$55$ per hour $($or any fraction thereof$).$

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a$.$ What is the utilization rate? $[$ Select $]["62\mathrm{.}5\%","79\mathrm{.}5\%","47\%","38\%","85\mathrm{.}3\%"]$

b$.$ What is the number of computers waiting to be serviced? $[$ Select $]["1\mathrm{.}23","\mathrm{.}66","2\mathrm{.}89","1\mathrm{.}67","1\mathrm{.}04"]$

c$.$ How long before a breakdown is serviced $($minutes$)[$ Select $]["\mathrm{.}75$ of an hour", $"\mathrm{.}67$ of an hour", $"25$ minutes", $"35$ minutes", $"40$ minutes"$]$

d$.$ Based on total system cost $($Ls$),$ what is the expected daily cost? $[$ Select $]["$$$2,166\mathrm{.}67","$$$216\mathrm{.}67","$$$2,045\mathrm{.}50","$$$182\mathrm{.}29","$$$1,822\mathrm{.}92"]$