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Thread: Maxima and minima problem

  1. #1
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    Maxima and minima problem

    A farmer has 4 km of fencing wire and wishes to fence a rectangular piece of land through which flows a straight river, which is to be utilised as one side of the enclosure. How can this be done to enclose as much land as possible?

    The actual answer is: 2 km x 1km = maximum of 2km2 but I keep getting 1km and 1km
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    Re: Maxima and minima problem

    Quote Originally Posted by julie9300 View Post
    A farmer has 4 km of fencing wire and wishes to fence a rectangular piece of land through which flows a straight river, which is to be utilised as one side of the enclosure. How can this be done to enclose as much land as possible?

    The actual answer is: 2 km x 1km = maximum of 2km2 but I keep getting 1km and 1km
    If we call $\displaystyle \displaystyle \begin{align*} x \end{align*}$ the width of the rectangle, and we know that the three sides of the rectangle that come from the fencing wire add up to 4km, then the length is $\displaystyle \displaystyle \begin{align*} 4 - 2x \end{align*}$.

    Thus, the area of the land is $\displaystyle \displaystyle \begin{align*} A = x(4 - 2x) = 4x - 2x^2 \end{align*}$.

    Now how would you find the maximum?
    Thanks from julie9300
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    Re: Maxima and minima problem

    Thanks!

    I realised my mistake, I kept calculating using four sides rather than three
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