$2.($ a $)$ ?A crew of mechanics at the Highway Department garage repair vehicles that break down at

? an average of $12$ ?vehicles per hour $($ approximately Poisson in nature $).$ ?The mechanic crew can

? service an average of $4$ ?vehicles every $10$ ?minutes with a repair time distribution that

? approximates an exponential distribution. The crew cost is approximately $ $50$ ?per hour. The

? cost associated with lost productivity from the breakdown is estimated at $ $80$ ?per vehicle per

? hour $($ or any fraction thereof $).$ ?Which is cheaper, the existing system with one service crew, or

? a revised system with two service crews? The average waiting time for adding the second crew

? is $0\mathrm{.}02.[5$ ?points $]$