document.write( "Question 1198520: The owner of the local apple orchard estimates that if 24 trees are planted per acre, then each mature tree will yield 648 apples per year. for each additional tree planted per acre the number of apples produced by each tree decreases by 12 per year. how many trees should be planted per acre to obtain the most apples per year? \n" ); document.write( "

Algebra.Com's Answer #832136 by ikleyn(52786) $\"\"$ $\"About$

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\n" ); document.write( "The owner of the local apple orchard estimates that if 24 trees are planted per acre,
\n" ); document.write( "then each mature tree will yield 648 apples per year.
\n" ); document.write( "for each additional tree planted per acre the number of apples produced
\n" ); document.write( "by each tree decreases by 12 per year. how many trees should be planted per acre
\n" ); document.write( "to obtain the most apples per year?
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document.write( "If the number of trees is 24+n, then the number of apples is 648-12n in each tree.\r\n" );
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document.write( "Total number of apples is thus  (24+n)*(648-12n).      (1)\r\n" );
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document.write( "We want to find \"n\" such that the quadratic function  (1)  has maximum value.\r\n" );
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document.write( "The maximum of a quadratic form is reached half-way between its zeroes.\r\n" );
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document.write( "The zeroes of the function (1) are -24 and 648/12 = 54.\r\n" );
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document.write( "Half-way between these numbers is   =  =  = 15.\r\n" );
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document.write( "The value of the quadratic function (1) is then  (24+15)*(648-12*15) = 18252.\r\n" );
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document.write( "ANSWER.  24+15 = 39 trees and 18252 apples.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Be attentive when you interpret the obtained solution:\r
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\n" ); document.write( "\n" ); document.write( " 15 trees per acre should be added to existing 24 trees per acre, \r
\n" ); document.write( "\n" ); document.write( " making all planted trees number 39 per acre.\r
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