Algebra.Com's Answer #793113 by ikleyn(52787)![\"\"](\"/images/stars/stars-13.gif\")  
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document.write( "Minimize z=4x+7y subject to x-y > 1, 3x+2y > 18, x > 0, y > 0.
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document.write( "First inequality x-y > 1 is THIS restriction\r\n" );
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document.write( " y < x - 1.\r\n" );
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document.write( "Second inequality 3x+2y > 18 is THIS restriction\r\n" );
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document.write( " y >  .\r\n" );
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document.write( "Together with the inequalities x > 0, y > 0 they form THIS feasibility domain in the first quadrant QI, shown in the Figure below:\r\n" );
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document.write( " Plot y < x-1 (under the read line) and y > (over the green line)\r\n" );
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document.write( "Feasibility domain is INFINITE AREA in Q1 UNDER the red line and over the green line.\r\n" );
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document.write( "Notice that x-axis y= 0 is not included into the feasibility domain since we have strict inequality y > 0 given.\r\n" );
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document.write( "The red and the green lines ALSO are not included into the feasibility domain, since the given inequalities are strict inequalities.\r\n" );
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document.write( "It implies that the given objective function HAS NO minimum in the assigned domain:\r\n" );
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document.write( " for any point in the domain, there is another point in the domain\r\n" );
document.write( " where the objective function has lesser value.\r\n" );
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document.write( "ANSWER. With given restrictions, the posted problem HAS NO SOLUTION.\r\n" );
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document.write( "Solved.\r
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document.write( "You, probably, will be very surprised with my conclusion,\r
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document.write( "but the real cause is that you INCORRECTLY wrote the restrictions in your post.\r
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document.write( "In order the problem would have the solution,
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document.write( "all the inequalities in the condition MUST BE \" >= \", --- not \" > \".\r
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