Q. A company has started a phone service that uses overseas doctors to provide emergency medical consultations. Responding doctors are based in a country with low wages but with a highly skilled pool of physicians. Responding to each call takes on average 15 minutes. At any given time, re are 4 doctors overseas on duty. Calls arrive every 5 minutes on average (standard deviation is 5 minutes). Company receives $50 from patient's insurance company for each consultation. If one of 4 overseas doctors is available, firm pays $20 to doctor and makes $30 in profit. If no doctor is available overseas, call is rerouted to U.S. where a local physician answers question. A local physician is always available to take a call. In this case, firm pays $50 to local physician, so there's no profit for company.

(a) What is probability of a call being answered by a physician in US?

(b) What would be additional revenue per hour obtained if company managed to have 10 doctors overseas on duty at any given time?

(c) What would be additional profit if company managed to have 10 doctors overseas on duty at any given time?