ty in advance !

Answer the questions 11-19 based on the following data. Pete's Market is a small local grocery store with only one checkout counter. Assume that shoppers arrive at the checkout lane according to a Poisson probability distribution, with an arrival rate of 13 customers per hour. The checkout service times follow an exponential probability distribution, with a service rate of 20 customers per hour. It is the manager's service goal to limit the waiting time prior to beginning the checkout process to no more than five minutes. After reviewing the waiting line analysis of his store, the manager of Pete's Market wants to consider one of the following alternatives for improving service. Option 1: Hire a second person to bag the groceries while the cash register operator is entering the cost data and collecting money from the customer. With this improved single-server operation, the service rate could be increased to 30 customers per hour. (Note: Although we hire one more person, it is still an M/M/1 queueing system, Because we do not operate a second counter but only hire a person to help with the first cashier counter, the service rate of the cashier improves.) Option 2: Hire a second person to operate a second checkout counter. The two-server operation would have a service rate of 20 customers per hour for each server. (Note: Since we know have two checkout counters, the system is upgraded to an M/M/k waiting-line system.) Think about the scenario in Option 2. What is the probability that no units are in the system? Po = 0.4286 Po = 0.6095 Po = 0.1524 Po = 0.0381 Think about the scenario in Option 2. What is the average number of units in the waiting line? A. Lq = 0.4826 B. Lq = 0.1524 C. Lq = 0.0095 D. Lq = 0.6095 Think about the scenario in Option 2. What is the average time a unit spends in the waiting line? A. Wq = 0.1524 hours (9.14 minutes) B. Wq = 0.0381 hours (~2.3 minutes) C. Wq = 0.0095 hours (=0.57 minutes) D. Wq = 0.6095 hours (= 36.57 minutes) Think about the scenario in Option 2. The average waiting time goal is 5 minutes or less. Does Option 1 meet the service goal with Wq s 5 minutes? No Yes