Anonymous
Anonymous asked in Science & MathematicsMathematics · 1 month ago

can you please help with this question?

Carly has just opened her nail salon. Based on experience, she knows that her daily profit,P, in dollars, can be modeled by the relation P = −15x²+ 240x − 640, where x is the number of clients per day. How many clients should she book each day to maximize her profit?

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  • alex
    Lv 7
    1 month ago

    Rule:

    P(x)=ax^2 + bx + c , with a<0---> maximum at x = -b/(2a)

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  • 1 month ago

    P is at a maximum where P '(x) = 0 and P ''(x) < 0.

    P '(x) = -30x + 240

    0 = -30x + 240

    x = 8

    P ''(x) = -30 for all x so we know the maximum occurs at x = 8.

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