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Math Help - max min problem

  1. #1
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    max min problem

    rectangular plot of farm land will be bounded on one side by a river and the other 3 sides by a single strand of electric wire. With 800 metres of wire at your disposal what is the largest area you can enclose and what are its dimensions.

    my answers : 80000m^2

    1st I let the perimeter = 800
    2y+x= 800

    then i subbed into the equation for the area A=xy and let it equal to zero.
    but i got to differentiate is this wrong?
    could someone verify my anwer?
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  2. #2
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    Re: max min problem

    Quote Originally Posted by raoulduke1 View Post
    rectangular plot of farm land will be bounded on one side by a river and the other 3 sides by a single strand of electric wire. With 800 metres of wire at your disposal what is the largest area you can enclose and what are its dimensions.

    my answers : 80000m^2

    1st I let the perimeter = 800
    2y+x= 800

    then i subbed into the equation for the area A=xy and let it equal to zero.
    but i got to differentiate is this wrong?
    could someone verify my anwer?
    You need the area to only be a function of one variable.

    From the first equation, you have \displaystyle 2y+x = 800 \implies y = 400 - \frac{1}{2}x, so substituting into the second gives

    \displaystyle \begin{align*} A &= xy \\ A &= x\left(400 - \frac{1}{2}x\right) \\ A &= 400x - \frac{1}{2}x^2 \\ \frac{dA}{dx} &= 400 - x \end{align*}

    Now set the derivative equal to \displaystyle 0, solve, back-substitute, solve for \displaystyle y.
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