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Ask iit jee aieee pet cbse icse state board community Community Discussion Question: maxima minima
Forum Index -> Differential Calculus like the article? email it to a friend.  
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jic (5)

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armer Gray owns productive cropland that abuts a highway. But the land that is 25 meters or more from the highway is yields twice as much per square meter as the land that is within 25 meters of the highway. Farmer Gray wants to fence-in some of the land to keep the farm animals out. Zoning regulations require that one section of any fence be right along the highway. Farmer Gray has only 600 meters of fencing material. If he fences a rectangular area, what are the dimensions of the rectangle that maximizes the total yield of the fenced-in land (assume that the highway is straight).

    
pink_ele (1235)

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Olaaa!! Perrrfect answer. 203  [313 rates]

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let length=x
and breadth=y
then 2(x+y)=600
x+y=300
y=300-x
now
yield per sq meter widin 25 kms =k
den yeild per sq km after 25 kms =2k
total yeild
Y=2k(300-x)(x-25)+25(300-x)k
diff w r t x nd equating
we get
x=625/4 for max yied
dimensions
625/4 and
575/4

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