document.write( "Question 1194596: A farmer owns a 100 acre farm and plans to plant at most three crops. The seed for crops A,B, and C costs $40, $20, and $30 per acre, respectively. A maximum of $3200 can be spent on the seed. Crops A,B, and C require 1,2, and 1 work days per acre, respectively, and there are a maximum of 160 workdays available. If the farmer can make a profit of $100 per acre on crop A, $300 per acre on crop B, and $200 per acre on crop \r
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Algebra.Com's Answer #826834 by ikleyn(52803) $\"\"$ $\"About$

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\n" ); document.write( "A farmer owns a 100 acre farm and plans to plant at most three crops.
\n" ); document.write( "The seed for crops A,B, and C costs $40, $20, and $30 per acre, respectively.
\n" ); document.write( "A maximum of $3200 can be spent on the seed.
\n" ); document.write( "Crops A,B, and C require 1,2, and 1 work days per acre, respectively,
\n" ); document.write( "and there are a maximum of 160 workdays available.
\n" ); document.write( "If the farmer can make a profit of $100 per acre on crop A, $300 per acre on crop B,
\n" ); document.write( "and $200 per acre on crop
\n" ); document.write( "Formulate LPP
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\n" ); document.write( "\n" ); document.write( "Solution\r
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document.write( "x acres of crop A;\r\n" );
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document.write( "y acres of crop B;\r\n" );
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document.write( "z acres of crop C.\r\n" );
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document.write( "The profit function\r\n" );
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document.write( "P(x,y,z) = 100x + 300y + 200z        (1)    (= objective function, dollars)\r\n" );
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document.write( "Restrictions:\r\n" );
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document.write( "  x +     y   +    z    <=  100      (2)    (total area, acres)\r\n" );
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document.write( "40x +   20y   +  30z    <= 3200      (3)    (cost of seed, dollars)\r\n" );
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document.write( "1x  +    2y   +   1z    <=  160      (4)    (workdays)\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( "and use 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 / (the \"simplex 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 = 0 (acres for A);  Y = 60 acres for B;  Z = 40 acres for C;  p = $26000.    ANSWER\r\n" );
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\n" ); document.write( "\n" ); document.write( "The input to the solver is shown/presented/documented below :\r
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document.write( "Maximize p = 100x + 300y + 200z subject to\r\n" );
document.write( "x   +    y   +    z    <=  100 \r\n" );
document.write( "40x +  20y   +  30z    <= 3200\r\n" );
document.write( "1x  +   2y  +    1z    <=  160\r\n" );
document.write( "x >= 0  \r\n" );
document.write( "y >= 0\r\n" );
document.write( "z >= 0\r\n" );
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