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Thread: Calc - Extreme Values - Word Problem

  1. #1
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    Calc - Extreme Values - Word Problem

    The profit, P, in dollars for selling x hamburgers is modelled by $\displaystyle P(x)= 2.44x - \frac {x^2}{20 000} - 5 000$, where $\displaystyle 0 \leq x \leq 35 000$. For what quantities of hamburgers is the profit increasing and decreasing?


    $\displaystyle P'(x) = 2.44 - 40000x $

    $\displaystyle 0 = 2.44 - 40 000x$

    $\displaystyle 6.1^{-0.5} = x$

    $\displaystyle P(6.1^{-0.5}) = -4999$

    $\displaystyle P(0) = -5000$

    $\displaystyle P(35 000) = 19 150$


    Therefore, decreasing at $\displaystyle (0, -5000) $ and increasing at $\displaystyle (35 000, 19 150)$



    Textbook Answer:
    increasing - $\displaystyle 0 \leq x \leq 24 400$
    decreasing - $\displaystyle 24 400 \leq x \leq 35 000$
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  2. #2
    Moo
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    Hello,

    Quote Originally Posted by Macleef View Post
    The profit, P, in dollars for selling x hamburgers is modelled by $\displaystyle P(x)= 2.44x - \frac {x^2}{20 000} - 5 000$, where $\displaystyle 0 \leq x \leq 35 000$. For what quantities of hamburgers is the profit increasing and decreasing?


    $\displaystyle P'(x) = 2.44 - {\color{red}40000x} $ << SiMoon says : it should be $\displaystyle \frac{x}{10000}$ !!

    $\displaystyle 0 = 2.44 - 40 000x$

    $\displaystyle 6.1^{-0.5} = x$ << SiMoon says : if you were right, it would have been $\displaystyle 6.1 \cdot {\color{red}10^5}$ !

    $\displaystyle P(6.1^{-0.5}) = -4999$

    $\displaystyle P(0) = -5000$

    $\displaystyle P(35 000) = 19 150$


    Therefore, decreasing at $\displaystyle (0, -5000) $ and increasing at $\displaystyle (35 000, 19 150)$



    Textbook Answer:
    increasing - $\displaystyle 0 \leq x \leq 24 400$
    decreasing - $\displaystyle 24 400 \leq x \leq 35 000$
    Therefore, there are problems all along :/
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  3. #3
    Eater of Worlds
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    Check your derivative.

    $\displaystyle P'(x)=\frac{61}{25}-\frac{x}{10,000}$

    $\displaystyle \frac{61}{25}-\frac{x}{10,000}=0$

    $\displaystyle x=24,400$

    Now check the slope on either side.
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