Week 5 Problem Set Use the WAITING_LINES.xlsx file to solve the following: ASSIGNED PROBLEM 1: The Peachtree Airport in Atlanta serves light aircraft. It has a single runway and one air traffic controller to land planes. It takes an airplane 10 minutes to land and clear the runway, but planes arrive at the rate of 4 per hour. 1a) What is the average number of planes that will stack up waiting to land? 1b) What is the average time (IN MINUTES) a plane must wait in line before it can land? 1c) What is the percent chance (i.e., the probability) that no planes are in the area and the traffic controller can actually take a breather? 1d) What is the average time (IN MINUTES) it takes a plane to clear the runway once it has notified the airport that it is in the vicinity and wants to land? 1e) If the FAA requires 15 minutes of idle time every hour for their Air Traffic Controllers (75% utilization), will the airport have to hire an extra air traffic controller? ASSIGNED PROBLEM 2: The Patriots ticket office receives 75 calls per hour. Each of their 4 sales reps can handle an average of 20 calls per hour, but there is a very large queue to keep customers on hold. 2a) What is the probability that no customers are on the phones? 2b) What is the average number of customers waiting to speak to a sales rep? 2c) What is the average time (IN MINUTES) a customer can expect to wait to speak with a sales rep? 2d) What percent of the time are the sales reps busy? 2e) What is the average number of customers on the phones at any time? 2f) What is the average time (IN MINUTES) a customer can expect to spend on the phone? 2g) What is the percent chance (i.e., the probability) that there are more than 5 customers on the phones? ASSIGNED PROBLEM 3: The Pizza On Demand store can bake 3 pies in 15 minutes (12 per hour). During most hours they average 8 customers per hour. They operate 10 hours per day, 7 days a week. Answer the following using waiting lines: 3a) What is the average # of minutes a customer can expect to wait before placing an order? 3b) What is the average number of customers in the store at one time? 3c) What percent of the time are the employees busy making pizza? 3d) What is the probability that more than 2 customers would be in the store at once (express as a percent)? ASSIGNED PROBLEM 4: The campus Career Center has been quite a hit. Lately they have been helping students with writing resumes, for which their 3 employees each average about 30 minutes per resume. Students have been showing up at a rate of about one every 15 minutes. 4a) What is the average time in minutes that a student can expect it to take to walk out with a completed resume after their arrival? 4b) What is the average number of students at the Career Center? 4c) What percent of the time is the Career Center empty?