Question 945997
A farmer wishes to put a fence around a rectangular field and then divide the field into three rectangular plots by placing two fences parallel to one of the sides. If the farmer can afford only 1000 yards of fencing, what dimensions will give the maximum rectangular area?
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Draw the picture.
There are 4 equal pieces and 2 OTHER equal pieces::
4x + 2y = 1000 yds
2x + y = 500
y = -2x+500
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Area = x*y
A = x(-2x+500)
A = -2x^2 + 500x
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Maximum A occurs when x = -b/(2a) = -500/(2*-2) = 125 yds
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Solve for "y"::
y = -2x+500
y = -2*125+500 = 250 yds
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Cheers,
Stan H.
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