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Thread: Applied Max/ Min Problems

  1. #1
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    Applied Max/ Min Problems

    A rectangular garden laid out along a neighbour's lot contains 432 m^2. It is to be fenced on all sides. If the neighbour pays for half the shared fence, what should be the dimensions of the garden so that your cost is a minimum??

    This is area = A'=0 is the derivative/
    So A = l x w...........................so notes on the side is w x l = 432.

    Where I am stuck is that do I take half of L and half of W for the equation??
    So I use A = l/2 X w/2??

    Answer is 18 x 24 m.
    STUCK!!
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  2. #2
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    total cost is based on the perimeter of the garden ...

    $\displaystyle C_T = 2L + 2W$

    let $\displaystyle L$ be the shared side ... neighbor's cost is $\displaystyle \dfrac{L}{2}$ . Your cost ...

    $\displaystyle C = \dfrac{3L}{2} + 2W$

    note that $\displaystyle W = \dfrac{432}{L}$ ...

    $\displaystyle C = \dfrac{3L}{2} + \dfrac{864}{L}$

    find $\displaystyle C'$ and determine the value of $\displaystyle L$ that minimizes $\displaystyle C$
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