Maximum and minimum quadratics

AO2005

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Oct 17, 2021
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I am not quite sure where to start with this problem.

A large hotel has 250 rooms. mangementt has determined that if they charge $150 per room on Saturday night, they will book 210 rooms. For every $15 increase in the room price, 10 less rooms will be booked. What price should the hotel charge to maximize their revenue?
 
I am not quite sure where to start with this problem.

A large hotel has 250 rooms. mangementt has determined that if they charge $150 per room on Saturday night, they will book 210 rooms. For every $15 increase in the room price, 10 less rooms will be booked. What price should the hotel charge to maximize their revenue?
Start with the expression for the total revenue as a function of the room price. The use methods you've been taught to find its maximum.
 
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