document.write( "Question 251958: The following maximum problem is in standard form. Introduce slack variables and set up the initial simplex.\r
\n" ); document.write( "\n" ); document.write( " Maximize P = 2x^1 + 4x^2 + x^3
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\n" ); document.write( " Subject to the constraints:
\n" ); document.write( "x^1 + x^2 + x^3 <= 12
\n" ); document.write( "x^1 ≥ 0
\n" ); document.write( "x^2 ≥ 0
\n" ); document.write( "x^3 ≥ 0
\n" ); document.write( "x^1 + x^2 <= 6
\n" ); document.write( "2x^1 - x^2 + 3x^3 <= 6
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Algebra.Com's Answer #184093 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
The following maximum problem is in standard form. Introduce slack variables and set up the initial simplex.
\n" ); document.write( "Maximize P = 2x1 + 4x2 + x3\r
\n" ); document.write( "\n" ); document.write( "Subject to the constraints:
\n" ); document.write( "x1 + x2 + x3 <= 12
\n" ); document.write( "x1 ≥ 0
\n" ); document.write( "x2 ≥ 0
\n" ); document.write( "x3 ≥ 0
\n" ); document.write( "x1 + x2 <= 6
\n" ); document.write( "2x1 - x2 + 3x3 <= 6\r
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document.write( "x1 + x2 + x3 + s1 = 12\r\n" );
document.write( "x1 + x2 + s2 = 6\r\n" );
document.write( "2x1 - x2 + 3x3 + s3 = 6\r\n" );
document.write( "P = 2x1 + 4x2 + x3\r\n" );
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document.write( "Write that as this system:\r\n" );
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document.write( " 1x1 + 1x2 + 1x3 + 1s1 + 0s2 + 0s3 + 0P = 12\r\n" );
document.write( " 1x1 + 1x2 + 0x3 + 0s1 + 1s2 + 0s3 + 0P =  6\r\n" );
document.write( " 2x1 - 1x2 + 3x3 + 0s1 + 0s2 + 1s3 + 0P =  6\r\n" );
document.write( "-2x1 - 4x2 - 1x3 + 0s1 + 0s2 + 1s3 + 1P =  0\r\n" );
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document.write( "Then make this as the first tableau:\r\n" );
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document.write( " x1 x2 x3  s1 s2  s3  P\r\n" );
document.write( "_____________________________\r\n" );
document.write( "| 1  1  1 | 1  0  0 | 0 | 12 |\r\n" );
document.write( "| 1  1  0 | 0  1  0 | 0 |  6 |\r\n" );
document.write( "| 2 -1  3 | 0  0  1 | 0 |  6 |\r\n" );
document.write( "|----------------------------|\r\n" );
document.write( "|-2 -4 -1 | 0  0  1 | 1 |  0 |\r\n" );
document.write( "ŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻ\r\n" );
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document.write( "The first step will be to select the most negative\r\n" );
document.write( "indicator which is -4. so the pivot column is the\r\n" );
document.write( "2nd column. \r\n" );
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document.write( "Divide each positive number above the -4 into the\r\n" );
document.write( "corresponding element in the far right:\r\n" );
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document.write( " ___         __ \r\n" );
document.write( "1)12 = 12,  1)6 = 6, 6 is smaller so pivot on the 1\r\n" );
document.write( "in the 2nd row 2nd column. \r\n" );
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document.write( "Edwin
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