а clerk takes orders by telephone. If the pied on one line, incoming phone calls to the catalog department are answered automatically by a record- ing machine and asked to wait. As soon as the clerk is free, the party that has waited the longest is trans- ferred and answered first. Calls come in at a rate of about 12 per hour. The clerk is capable of taking order in an average of 4 minutes. Calls tend to fol- low a Poisson distribution, and service times tend to be exponential. The clerk is paid $10 per hour, but because of lost goodwill and sales, Ashley's loses about $50 per hour of customer time spent waiting for the clerk to take an order 12-19 Juhn and Son one worker v company truc an average of a Poisson dis an rate of 4 per nential distrib Determi loading gate there will b loaded or wa ing model cc (a) What is the average time that catalog customers must wait before their calls are transferred to the order clerk? 12-20 Juhn believ will substan estimates th (b) What is the average number of callers waiting to place an order? (c) Ashley's is considering adding a second clerk to take calls. The store would pay that person the same $10 per hour. Should it hire another clerk? Explain. single-serve the loading per hour. Ar change and Problem 12 12-21 Truck driver lems 12-19 12-17 Automobiles arrive at the drive-through window at a post office at the rate of four every 10 minutes. The average service time is 2 minutes. The Poisson dis- tribution is appropriate for the arrival rate and ser- vice times are exponentially distributed. hour on ave hour. Truck loading gat tively idle that time. W (a) What is the average time a car is in the system? (b) What is the average number of cars in the system? (c) What is the average time cars spend waiting to the firm as stead of one receive service? 12-22 Juhn (of Pr second plat ing the fru (d) What is the average number of cars in line be- hind the customer receiving service? (e) What is the probability that there are no cars at the window? more effici (f) What percentage of the time is the postal clerk busy? (g) What is the probability that there are exactly two cars in the system? help out the Assum be able to will contin the waiting 12-18 For the post office in Problem 12-17, a second drive- through window is being considered. A single line new appro considered