Question 941547: A farmers has 400 feet of fencing to make three rectangular pens. What dimensions x and y will maximize the total area?
Answer by TimothyLamb(4379)   (Show Source):
You can put this solution on YOUR website! assume that the three pens are not adjacent:
assume that each pen needs four complete sides:
assume that all three pens have the same dimensions:
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length of fencing needed for each pen = 400/3 = 133.333333333 ft
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2x + 2y = 133.333333333
2y = 133.333333333 - 2x
y = (133.333333333 - 2x)/2
y = 133.333333333/2 - x
y = 66.6666666666 - x
a = xy
a = x(66.6666666666 - x)
a = 66.6666666666x - xx
-xx + 66.6666666666x = 0
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the above quadratic equation is in standard form, with a=-1, b=66.6666666666 and c=0
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-1 66.6666666666 0
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the quadratic has a vertex maximum at: ( 33.3333333, 1111.11111 )
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area for each pen is maximum (1111.11111 sq.ft) when x = 33.3333333 ft
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answer:
the dimensions of each of the three pens are:
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x = 33.3333333333 ft
y = 66.6666666666 - x
y = 66.6666666666 - 33.3333333333
y = 33.3333333333 ft
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