Thereafter, the patients are parsed into two categories: $20\%$ of all patients that come into the ED are trauma victims that need to be placed in a trauma bay. The other $80\%$ of the patients go into normal examination rooms. Each trauma patient spends an average of $30$ minutes in a trauma bay before leaving the ED $($usually then being admitted to the main part of the hospital$),$ whereas non$-$trauma patients spend an average of $45$ minutes in an examination room before leaving the ED$.$

Q$11.$ Suppose on average $50$ patients come to the emergency department every hour. What is the implied utilization $($in $\%)$ at the trauma bays? Recall there are $3$ trauma bays. Round your answer to the nearest whole number. Q$13$Which resource is the bottleneck?