Please fully answer the question and show your work please

6. Recall that the equilibrium (optimal) utilization gives us the point at which the excess capacity 4- put equals the mean queue size (average number in the queue) E[14]. To help the theme park manager, we can solve the optimal utilization p in terms of s by expressing pas (1/s)/, since each server is expected to take on 1/s' arrivals. The result is: (+1) ? What is the optimal staffing level (mumber of servers)? 7. For any one of the individuals queues, what is the utilization of the server at the optimal staffing level (optimal utilization)? 8. Considering any one of the individual s* queues, derive the expected waiting time (seconds) spent in line for a customer