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$).$

$$

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

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

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

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