QUESTION 4 (20 POINTS) Tony Soprano sits at a table in the back of Corleone's Grille and Pub waiting for visitors. If the chair opposite Mr. Soprano is occupied, visitors wait at the bar. When the chair becomes free, the next visitor sits down and talks to Mr. Soprano. Visitors arrive at a rate of 14 per hour, and the arrival pattern follows an exponential distribution. Once seated, the visitor does not leave until Mr. Soprano has finished the conversation. Mr. Soprano is quite unpredictable, and the lengths of his conversations tend to follow an exponential distribution with a mean time of 3 minutes. Once the conversation is over, the visitor always leaves the restaurant. areas toso per m (a) Each visitor has a taxi waiting outside. How much will each pay, on average, to keep the taxi waiting while they are in the restaurant? Assume that a taxi charges 0.60 per minute to wait. Recently, Tony's business has picked up substantially, and his visitors have been arriving at the restaurant at a rate of 40 per hour (again following an exponential distribution). Tony has found that when his visitors wait at the bar, it costs him approximately 40 per hour per visitor since the visitors all put drinks on his tab. To stem the increasing bar tab, Tony has decided to hire assistants to hold conversations for him. Now, Tony no longer holds conversations. Rather, he watches the assistants (who work considerably slower than he did) to ensure that each maintains a mean conversation time of 5 minutes (exponentially distributed). Assume that visitors at the bar go to whichever assistant is available first. (b) If Tony can use four, five, or six assistants to hold his meetings, how many assistants should he hire? Assume that each assistant gets paid 25 per hour, regardless of how busy they are. Start by listing the costs that are relevant for your calculations