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If Exactly 150 People Sign Up for a Charter Flight

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If exactly 150 people sign up for a charter flight, Leisure World Travel Agency charges $250/person. However, if more than 150 people sign up for the flight (assume this is the case) , then each fare is reduced by $1 for each additional person. Determine how many passengers will result in a maximum revenue for the travel agency. What is the maximum revenue? What would be the fare per passenger in this case?
Hint: Let x denote the number of passengers above 150. Show that the revenue function R is given by R(x) = (150 + x) (250 - x) .


Definitions:

Broadcast Medium

Any medium used to transmit information, entertainment, or other messages to a wide audience, typically involving radio, television, or the internet.

Infrared

A type of electromagnetic radiation with wavelengths longer than visible light but shorter than microwaves, used in devices like remote controls and thermal imaging cameras.

Twisted-pair

A type of cabling that consists of pairs of insulated wires twisted together, commonly used for telecommunication and network connections.

Cable Medium

A type of physical transmission medium that uses cables, such as coaxial or fiber optic, to transmit data.

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