document.write( "Question 1151279: A farmer has 1000 acres of land on which he can grow corn, wheat and soybean. Each acre of corn costs birr 100 for preparation, requires 7 man-days work and yields a profit of birr 30. An acre of wheat costs birr 120 to prepare, requires 10 man-days of work and yields a profit of birr 20. An acre of Soybeans costs birr 70 to prepare, requires 8 man-days of work and yields a profit of birr 20. If the farmer has birr 100,000 for preparation and can count on 8000 man-days of work, how may acres should be allocated to each crop to maximize profit? \n" ); document.write( "
Algebra.Com's Answer #773035 by ikleyn(52785)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "x acres for corn;\r\n" );
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document.write( "y acres for wheat;\r\n" );
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document.write( "z acres for soybeans.\r\n" );
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document.write( "The profit function\r\n" );
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document.write( "P(x,y,z) = 30x + 20y + 20z            (1)    (= objective function)\r\n" );
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document.write( "Restrictions:\r\n" );
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document.write( "x   +     y +   z <= 1000             (2)   (1000 acres in all)\r\n" );
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document.write( "100x + 120y + 70z <= 100000           (3)   (cost for preparation)\r\n" );
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document.write( "7x   +  10y +  8z <= 8000             (4)   (man-days work)\r\n" );
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document.write( "x >= 0,  y >= 0,  z >=  0             (5)   (standard non-negativity restrictions)\r\n" );
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document.write( "Now go to the site https://www.zweigmedia.com/RealWorld/simplex.html\r\n" );
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document.write( "                   https://www.zweigmedia.com/RealWorld/simplex.html\r\n" );
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document.write( "and use the free of charge solver there.\r\n" );
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document.write( "Input the profit function and the restrictions and press the \"Solve\" button.\r\n" );
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document.write( "It will solve this maximization problem using the Linear Programming method.\r\n" );
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document.write( "The solver produces this solution (this answer)\r\n" );
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document.write( "   X = 1000 acres;  Y = 0 acres;  Z = 0 acres;  p = 30000.    ANSWER\r\n" );
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document.write( "Maximize p = 30x + 20y + 20z subject to\r\n" );
document.write( "x + y + z <= 1000 \r\n" );
document.write( "100x + 120y + 70z <= 100000\r\n" );
document.write( "7x + 10y + 8Z <= 8000\r\n" );
document.write( "x >= 0  \r\n" );
document.write( "y >= 0\r\n" );
document.write( "z >= 0\r\n" );
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document.write( "For reliability purposes, I checked this solution by running another solver,\r\n" );
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document.write( "https://www.wolframalpha.com/widgets/view.jsp?id=daa12bbf5e4daec7b363737d6d496120\r\n" );
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document.write( "and obtained the same result.\r\n" );
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