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Airplanes Arrive for Take-Off at the Runway of an Airport

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Essay

Airplanes arrive for take-off at the runway of an airport according to a Poisson process at a mean rate of 20 per hour.The time required for an airplane to take off has an exponential distribution with a mean of 2 minutes,and this process must be completed before the next airplane can begin to take off.Because a brief thunderstorm has just begun,all airplanes which have not commenced take-off have just been grounded temporarily.However,airplanes continue to arrive at the runway during the thunderstorm to await its end.Assuming steady-state operation before the thunderstorm,determine the expected number of airplanes that will be waiting to take off at the end of the thunderstorm if it lasts 30 minutes.

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Definitions:

Selling Expense

Costs incurred directly related to the sale of a product or service, including advertising, sales commissions, and store maintenance.

Unavoidable Waste

Waste that cannot be reduced or eliminated during the production process due to inherent limitations or efficiency constraints.

Unexpected Spoilage

Loss or waste of materials, products, or resources that occurs unexpectedly during the production process and is not a part of planned spoilage.

Normal Spoilage

Normal spoilage refers to the expected amount of waste or loss of materials during a production process, considered as a usual and unavoidable cost of doing business.

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