(14 points total) 1. Suppose a grocery store has collected data on customer arrivals to the checkout area and on the service times to check out during a busy period of the week. On average customers arnve to the checkout area at a rate of 45 per hour. On average, each server in the checkout area can serve (check out) 12 customers per hour. Assume Poisson arrivals and exponential service times (3 pts) 11. What is the minimum number of servers required? a) 2 b) 3 c) 4 d) none of the above. (3 pts ) 12. If there are 5 identical servers, then the average waiting time in line for a customer is in which range? a) less than 0.031 minutes b) 00311 minute. c) 1375 minutes d) 3768 minutes e) more than 8 minutes. (3 pts) 13. If there are 5 identical servers, then the average waiting time in the system for a customer is in which range? a) less than 0.031 minutes. b) 0.0311 minute c) 13.75 minutes. d) 3.768 minutes e) more than 8 minutes (5 pts.) 1.4. Suppose each server in the checkout area is identical in their rate of service, and each is paid \$1\$ per hour Also suppose that a customer's waiting time is valued at $12 per hour. How many servers should there be to minimize the total cost and what is the average total hourly cost to provide the service (including cost for the servers and cost for the customer's waiting time)? Number of servers = Average total hourly cost = (14 points total) 1. Suppose a grocery store has collected data on customer arrivals to the checkout area and on the service times to check out during a busy period of the week. On average customers arnve to the checkout area at a rate of 45 per hour. On average, each server in the checkout area can serve (check out) 12 customers per hour. Assume Poisson arrivals and exponential service times (3 pts) 11. What is the minimum number of servers required? a) 2 b) 3 c) 4 d) none of the above. (3 pts ) 12. If there are 5 identical servers, then the average waiting time in line for a customer is in which range? a) less than 0.031 minutes b) 00311 minute. c) 1375 minutes d) 3768 minutes e) more than 8 minutes. (3 pts) 13. If there are 5 identical servers, then the average waiting time in the system for a customer is in which range? a) less than 0.031 minutes. b) 0.0311 minute c) 13.75 minutes. d) 3.768 minutes e) more than 8 minutes (5 pts.) 1.4. Suppose each server in the checkout area is identical in their rate of service, and each is paid \$1\$ per hour Also suppose that a customer's waiting time is valued at $12 per hour. How many servers should there be to minimize the total cost and what is the average total hourly cost to provide the service (including cost for the servers and cost for the customer's waiting time)? Number of servers = Average total hourly cost =