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A company has started a phone service that uses overseas doctors to provide emergency medical consultations. The 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 moment in time, there are 4 doctors overseas on duty. Calls arrive every 5 minutes on average and standard deviation of the inter-arrival time is 5 minutes. The company receives $50 from the patient’s insurance company for each consultation. If one of the 4 overseas doctors is available, the firm pays $20 to the doctor and makes $30 in profit. If no doctor is available overseas, the call is rerouted to the U.S. where a local physician answers the question. A local physician is always available to take a call. In this case, the firm pays the $50 to the local physician, so there’s no profit for the company.
1. What is the percentage of calls being answered by a physician in the US? (Write the percentage, that is, if your answer is 53.22%, input 53.22 as the answer.)
2. How much (in $) does the company pay the physicians in the US over a 4 hour period?
3. What would be the additional profit (in $) per hour if the company managed to have 10 doctors overseas on duty at any given time?
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