Problem $4[15pts]$

Consider a waiting line system with the arrival rate being $10$ customers per hour and the service $on$ a customer $is12$ minutes $on$ average. Assume that both inter$-$arrival time and service time follow exponential distribution.

$(a)$ What's the arrival rate $$ and service rate $(customers$ per hour$)?[5pts]$

$(b)$ What $is$ the minimum number $of$ servers that are required $to$ ensure the customer's average waiting time $in$ queue $isno$ more than $5$ minutes? $[5pts]$

$(c)$ What $is$ the minimum number $of$ servers that are required $to$ ensure the average number $of$ people inthe system $isno$ more than $4?[5pts]$