Assignment:
Altug’s Coffee Shop decides to install an automatic coffee vending machine outside one of its stores to reduce the number of people standing in line inside. Mehmet Altug charges $3.50 per cup. However, it takes too long for people to make change. The service time is a constant 3 minutes, and the arrival rate is 15 per hour (Poisson distributed).
a) What is the average wait in line?
b) What is the average number of people in line?
c) Mehmet raises the price to $5 per cup and takes 60 seconds off the service time. However, because the coffee is now so expensive, the arrival rate drops to 10 per hour. Now what are the average wait time and the average number of people in the queue (waiting)?
Provide complete and step by step solution for the question and show calculations and use formulas.