document.write( "Question 969490: Juliet has 900 ft of fencing to build 6 animal pens. What dimensions for x and y maximize the total enclosed area? What is the total maximum area? What is the maximum size for one of the six animal pens?
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\n" ); document.write( "The diagram shown 2x3 rectangle with six animal pens inside. \n" ); document.write( "

Algebra.Com's Answer #592367 by josmiceli(19441) $\"\"$ $\"About$

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If the pens measure x by y then the
\n" ); document.write( "perimeter of each is $\"+2x+%2B+2y+\"$
\n" ); document.write( "The perimeters of $\"+6+\"$ pens measure
\n" ); document.write( " $\"+6%2A%28+2x+%2B+2y+%29+=+12%2A%28+x+%2B+y+%29+\"$
\n" ); document.write( " $\"+12%2A%28+x+%2B+y+%29+=+900+\"$
\n" ); document.write( " $\"+x+%2B+y+=+75+\"$
\n" ); document.write( " $\"+y+=+75+-+x+\"$
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\n" ); document.write( " $\"+A+=+x%2Ay+\"$
\n" ); document.write( " $\"+A+=+x%2A%28+75+-+x+%29+\"$
\n" ); document.write( " $\"+A+=+-x%5E2+%2B+75x+\"$
\n" ); document.write( "This is a parabola which is maximum when
\n" ); document.write( " $\"+x%5Bmax%5D+=+-b%2F%282a%29+\"$
\n" ); document.write( " $\"+x%5Bmax%5D+=+-75%2F%282%2A%28-1%29+%29+\"$
\n" ); document.write( " $\"+x%5Bmax%5D+=+37.5+\"$
\n" ); document.write( "and
\n" ); document.write( " $\"+y+=+75+-+x+\"$
\n" ); document.write( " $\"+y+=+37.5+\"$
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\n" ); document.write( "To maximize area, the dimensions of
\n" ); document.write( "each pen are: 37.5 x 37.5
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\n" ); document.write( "Here is a plot of the function $\"+A+=+-x%5E2+%2B+75x+\"$
\n" ); document.write( " $\"+graph%28+400%2C+400%2C+-10%2C+90%2C+-200%2C+1500%2C+-x%5E2+%2B+75x+%29+\"$
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