The Escargot is a small French restaurant with 6 waiters andwaitresses. The average service time at the restaurant for arunway (exponentially distributed). Planes arrive at theairport at the rate of 5 per hour (Poisson distributed).a.Determine the average number of planes that will stack up waiting to land.b.Find the average time a plane must wait in line before itcan land.c.Calculate the average time it takes a plane to clear therunway once it has notied the airport that it is in thevicinity and wants to land.d.The FAA has a rule that an air trafc controller can,onthe average,land planes a maximum of 45 minutes outof every hour. There must be 15 minutes of idle timeavailable to relieve the tension. Will this airport have tohire an extra air trafc controller? 5-7. The National Bank of Union City currently has one outsidedrive-up teller. It takes the teller an average of three min-utes (exponentially distributed) to serve a bank customer.Customers arrive at the drive-up window at the rate of 12per hour (Poisson distributed). The bank operations of-cer is currently analyzing the possibility of adding a sec-ond drive-up window at an annual cost of $20,000. It isassumed that arriving cars would be equally divided be-tween both windows. The operations ofcer estimates thateach minutes reduction in customer waiting time wouldincrease the banks revenue by $2000 annually. Should thesecond drive-up window be installed? What other factorsshould be considered in the decision besides cost? 5-8. During registration at Tech every quarter,students in theDepartment of Management must have their coursesapproved by the departmental advisor. It takes the advisoran average of ve minutes (exponentially distributed) toapprove each schedule,and students arrive at the advisersofce at the rate of 10 per hour (Poisson distributed). Com-pute L , Lq , W , Wq ,and . What do you think about thissystem? How would you change it? 5-9. All trucks traveling on Interstate 40 between Albuquerqueand Amarillo are required to stop at a weigh station. Trucksarrive at the weigh station at a rate of 120 per eight-hourday (Poisson distributed),and the station can weigh,on theaverage,140 trucks per day (Poisson distributed).a.Determine the average number of trucks waiting,the aver-age time spent at the weigh station by each truck,and theaverage waiting time before being weighed for each truck.b.If the truck drivers nd out they must remain at theweigh station longer than 15 minutes on the average,they will start taking a different route or traveling atnight,thus depriving the state of taxes. The state of New Mexico estimates it loses $10,000 in taxes peryear for each extra minute (over 15) that trucks mustremain at the weigh station. A new set of scales wouldhave the same service capacity as the present set of scales,and it is assumed that arriving trucks would lineup equally behind the two sets of scales. It would cost$50,000 per year to operate the new scales. Should thestate install the new set of scales? 5-10. In Problem 5-9(a),suppose arriving truck drivers look tosee how many trucks are waiting to be weighed at the table (of any size) is 80 minutes (exponentially distributed).The restaurant does not take reservations and parties arrivefor dinner (and stay and wait) every 16 minutes (Poisson dis-tributed). The restaurant is concerned that a lengthy waitingtime might hurt its business in the long run. What is thecurrent waiting time and queue length for the restaurant?Discuss the quality implications of the current waiting timeand any actions the restaurant might take