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Math Help - Revenue

  1. #1
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    Revenue

    The Hotel Summerfield has 500 rooms. Currently the hotel is filled . The daily rental is $ 850 per room.
    For every $ 16 increase in rent the demand for rooms decreases by 8 rooms.
    Let x = the number of $ 16 increases that can be made.
    What should x be so as to maximize the revenue of the hotel ? _______________
    What is the rent per room when the revenue is maximized? $_______________
    What is the maximum revenue? $_________________
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  2. #2
    Senior Member MaxJasper's Avatar
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    Re: Revenue

    $925 a night looks better!
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  3. #3
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    Re: Revenue

    Quote Originally Posted by spyder12 View Post
    The Hotel Summerfield has 500 rooms. Currently the hotel is filled . The daily rental is $ 850 per room.
    For every $ 16 increase in rent the demand for rooms decreases by 8 rooms.
    Let x = the number of $ 16 increases that can be made.
    If each room cost $850 (I'm not going to be staying there!) to start with, and there are x "$16 increases", what would the price per room be?
    If they initially rented all 500 rooms and the number of rooms decreased by 8 for each $16 increase, how many rooms will be rented with x "$16 increases"? The total revenue will be the number or rooms rented times the rent for each room.

    Once you have that "revenue function", do you know how to maximize a function?

    What should x be so as to maximize the revenue of the hotel ? _______________
    What is the rent per room when the revenue is maximized? $_______________
    What is the maximum revenue? $_________________
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