document.write( "Question 1189862: Solve the following problem by simplex method.
\n" ); document.write( "Max Z = 8x1 + 16x2
\n" ); document.write( "Subject to: x1 + x2  200
\n" ); document.write( " x2  125
\n" ); document.write( " 3x1 + 6x2  900
\n" ); document.write( " Where x1, x2  0 non-negativity condition\r
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Algebra.Com's Answer #849277 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "Solve the following problem by simplex method.
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\n" ); document.write( "Max Z = 8x1 + 16x2
\n" ); document.write( "Subject to: x1 + x2 <= 200
\n" ); document.write( " x2 <= 125
\n" ); document.write( " 3x1 + 6x2 <= 900
\n" ); document.write( " Where x1, x2 > 0 (non-negativity condition)
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\n" ); document.write( "\n" ); document.write( " It can be solved mentally, using common sense only
\n" ); document.write( " and without using the simplex method.\r
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document.write( "Indeed, from the objective function form  Z = 8x1 + 16x2 \r\n" );
document.write( "it is clear that it is profitable to keep x2 as large as possible due to constrains\r\n" );
document.write( "and after determining x2 in this way to keep x1 as large as possible due to the constrains.\r\n" );
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document.write( "Doing this way, we take  x2 = 125  (maximum allowed by the constrain x2 <= 125).\r\n" );
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document.write( "Then we determine x1 =  = 50 from constrain 3x1 + 6x2 <= 900.\r\n" );
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document.write( "Then   = 8x1 + 16x2 = 8*50 + 16*125 = 2400.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved mentally.\r
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