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In: Statistics and Probability

A restaurant that has a limited capacity of 30 people. The restaurant has an entrance fee...

A restaurant that has a limited capacity of 30 people. The restaurant has an entrance fee of $5/person. People arrive at this restaurant at a rate of 4/hour. The time each person spends in the restaurant follows an exponential distribution with rate ?. Suppose it costs 3? per hour for this restaurant to provide service to the customers. Find ? that maximizes the benefit of this restaurant.

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