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Maxima question needs checking

  1. Aug 2, 2009 #1
    question

    a rectangular plot of land requires fencing on all 4 sides. two opposite sides will use heavy duty fencing at £6/metre, whilst the other tow sides will use standard fencing at £3/metre. if the farmer buying the fencing has £5000 to spend, what is the maximum area he can enclose?

    attempt

    let y = heavy duty fencing sides and x= standard fencing sides.

    A=x*y
    5000=6y+6y+3x+3x
    5000=12y+6x...solve for x (or y)...
    5000-12y=6x (divide by 6)...
    833.33-2y=x....Now we will substitute this in to A=x*y

    A=(833.33-2y)*y
    A=833.33y-2y2 ....now take derivative and set equal to 0
    A'=833.33-4y=0
    or...4y=833.33
    y=208.33 meters.find x
    5000-(12*208.33)=6x
    2500=6x
    x=416.66 meters

    So max area is x*y or (208.33*416.66)= 86803m2.
     
  2. jcsd
  3. Aug 2, 2009 #2

    Gib Z

    User Avatar
    Homework Helper

    That is the correct method and solution. It may be slightly better to use the exact values, eg 2500/3, rather than 833.33, and also instead of differentiating and solving, you could use the formula for the axis of symmetry of a parabola x=-b/2a, might be quicker next time.
     
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