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Math Help - optimization

  1. #1
    Junior Member
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    optimization

    A 150 room hotel will rent all of its room if it charges $40 per room. The manager knows that for each $2 dollar increase per room, eight fewer room will be rented per night. What rent would maximize the revenue per night?

    I'm having trouble setting up the equation.
    I said w= each $2 dollar increase
    so revenue= (150-8w)(40+w)

    but this comes out wrong. I know w should =0, right. Any help would be great
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  2. #2
    Pim
    Pim is offline
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    Say we do a 2 dollar increase. According to your definition, w = 1. Therefore the hotel will rent out 150-8*1 = 142 rooms for 40+1=41 dollars per room (!).
    Do you see how you should correct your formula now?
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