question 1 a single ticket taker can tear tickets

Question

Question 1

1. A single ticket taker can tear tickets and direct movie patrons to their seats at a rate of 90 per hour. Customers arrive every minute for assistance and always wait, regardless of how long the line gets. Arrivals are governed by the Poisson distribution and service is governed by the exponential distribution.
   
   Use the information in Scenario. What is the probability that customers with tickets arrive and the ticket taker is not helping another patron?

Question 2

1. Weary travelers arrive at Will Rogers International Airport, pick up their luggage, stumble to their cars, and proceed to the parking lot attendant to pay for their parking. Traveler interarrival times are exponentially distributed, as are the service times of the attendant. On average, travelers arrive every 25 seconds. The attendant can process three travelers per minute.
   
   Use the information in Scenario. What is the probability that a traveler will pull up to the attendant's service window without having to wait for another customer?

Question 3

1. Weary travelers arrive at Will Rogers International Airport, pick up their luggage, stumble to their cars, and proceed to the parking lot attendant to pay for their parking. Traveler interarrival times are exponentially distributed, as are the service times of the attendant. On average, travelers arrive every 25 seconds. The attendant can process three travelers per minute.
   
   Use the information in Scenario. What is the average time a customer spends in line?

Question 4

Customers arrive at the one remaining full-service gas station in the country at the rate of 45 per minute and are served by the first available of three pump jockeys who can dole out gas and check oil at the rate of 20 customers per minute. Both service and interarrival times are governed by the exponential distribution. The probability that no pump jockey is busy is 0.0748.

1. Use the information in Scenario. What is the average time a customer spends in the system?

Question 5

1. Customers arrive at a ticket counter at the rate of 50 customers per hour, according to a Poisson distribution. There are three ticket agents. Customers select the first available agent from one line. Each agent can process 20 customers per hour with exponential service times.
   
   Use the information in Scenario. What is the average waiting time in line?

Question 6

1. A trucking firm has five trucks that each requires service at an average rate of once every 50 hours, according to an exponential distribution. The firm has a mechanic who needs five hours to complete the average job with exponential service times.
   
   Use the information in Scenario. What is the average utilization of the mechanic?

Question 7

1. A trucking firm has five trucks that each requires service at an average rate of once every 50 hours, according to an exponential distribution. The firm has a mechanic who needs five hours to complete the average job with exponential service times.
   
   Use the information in Scenario C.5. What is the average waiting time of trucks in line?

Question 8

1. The production rate has been steady at 20 units per hour. The average work-in-process inventory at this station is 15 units. What is the average lead time through this manufacturing station?

Question 9

1. Customers arrive at the local grocery store at a steady rate of 40 an hour. Thirty percent of these customers purchase 10 items or less and go to the express line where they enjoy an average checkout time of 5 minutes. Customers that don't meet the express line criterion go to checkout line #2 where they spend an average of 10 minutes checking out. How many people are checking out in line #2 on average? There are five cashiers serving line #2.

Question 10

1. Customers arrive at the local grocery store every 30 seconds on average. Thirty percent of these customers spend an average of 15 minutes shopping and purchase 10 items or less. These lucky customers go to the express line where they enjoy an average checkout time of 5 minutes. Customers that don't meet the express line criterion average 40 minutes in the store and go to checkout line #2 where they spend an average of 10 minutes checking out. How many people are checking out at any given time?There are four cashiers serving line #1 and 15 serving line #2.