Studying the congestion at the boat launching ramp on lake

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Reference no: EM132267852

The Town of Lake Wobegon has been studying the congestion at the boat launching ramp on the lake. On weekends the arrival rate averages five boats per hour, Poisson-distributed. The average time to launch or retrieve a boat is 10 minutes, with an exponential distribution. Assume only one boat can be launched or retrieved at a time.

In mid-afternoon, about half of the arriving boats are putting into the lake and the other half are pulling their boats out. There is a safety concern with having too many boats floating around waiting to be retrieved. On average, how many boats are floating around waiting to be retrieved?

A service organization (The Sons of Knut, Lodge 4011) is thinking about opening a concession stand at the ramp, and they need some estimate of potential demand. If the average boating party has three people in it, about how many people use the ramp between 6:00 a.m. and 8:00 p.m.?

The Sons of Knut estimate that they could sell $3 of concession items per boater on average, if the boater has to wait to use the ramp (however, if the boater has to wait more than 20 minutes to use the ramp she is only likely to spend $1). If she doesn’t have to wait at all, she is likely to spend $1.50. How much could the concession stand expect to take in between 6:00 a.m. and 8:00 p.m.? Show your work.

What assumptions did you have to make in order to use the model in answering questions A-F?

Reference no: EM132267852

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