A 440-unit hotel is trying to determine their daily rates. From experience, the hotel manager knows that all rooms are typically occupied when the daily room rate is $91. Market research indicates that for every increase of $\displaystyle {x}$ dollars in the daily room rate, there will be $\displaystyle {x}$ rooms vacant. Each occupied room costs $22 per day to service and maintain. What should the hotel charge per day in order to maximize profit?

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