Question 1 TORA Groceries operates with a maximum of three checkout counters. The manager uses the following schedule to determine the number of counters in operation, depending on the number of customers in line: Customers arrive in the counters area according to a Poisson distribution with a mean rate of 10 customers per hour. The average checkout time per customer at all counters are identical and exponential with mean 12 minutes. (a) Construct the rate diagram for this queueing system. [5] (b) Determine the values of P0 and P7. [10] (c) Determine the probability that only one counter will be opened. [5] (d) Determine the expected number of idle counters. [10]