Problem 5 (16 Marks) A take-out fast food restaurant located in a busy downtown area has one window open from 11:00am to 11:00pm cach day. It is found that every 10 minutes (in average), there is a customer coming to the restaurant. The average time to serve a customer (including time to place order, time to get food ready and time to pay the bill) is 4 minutes. It is also observed that both arrival and service processes follow Poison distributions. Use the standard queuing theory models discussed in class to evaluate the situation of the restaurant by calculating 5.1) the estimated time that the service window is busy serving customers in the 12 hours cach day 5.2) the expected time a customer will wait to get served after he/she arrives at the restaurant 5.3) the expected time a customer will spend at the restaurant (including waiting time and the time of being served) after he/she arrives at the restaurant 5.4) the estimated time that there are 2 or more customers in the restaurant in the 12 hours each day You may use the following equations in answering this question. System utilization: p = where A is customer arrival rate and He is the service rate. Expected time in queue: Ty Expected time in system T Probability that there are n customers in the system: P(n) = P(0) x 4" = (1-x)" H(NA) (2)