document.write( "Question 1138582: Minimize C=2x+3y+4z subject to minimize the problem:
\n" ); document.write( "4x+2y+z=10
\n" ); document.write( "x+y-z=5
\n" ); document.write( "x≥0,y≥0,z≥0 \n" ); document.write( "

Algebra.Com's Answer #756421 by ikleyn(52777) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "Minimize C = 2x + 3y + 4z subject to $\"highlight%28cross%28minimize%29%29\"$ $\"highlight%28cross%28the%29%29\"$ $\"highlight%28cross%28problem%29%29\"$ restrictions:
\n" ); document.write( "4x + 2y + z = 10
\n" ); document.write( " x + y - z = 5
\n" ); document.write( "x ≥ 0, y ≥0, z ≥ 0
\n" ); document.write( "~~~~~~~~~~~~~~~~~~~~~~~~~~~\r
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document.write( "4x + 2y + z = 10       (1)\r\n" );
document.write( " x +  y - z =  5       (2)\r\n" );
document.write( "x ≥ 0, y  ≥0, z ≥ 0\r\n" );
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document.write( "The idea of the solution is THIS: \r\n" );
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document.write( "    The given system of two equations defines a straight line in the space (x,y,z), which is the intersection \r\n" );
document.write( "    of the two relevant planes in .\r\n" );
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document.write( "    I am going to express this straight line as a parametric line of one argument and then express the OBJECTIVE function \r\n" );
document.write( "    as the function of the same argument\r\n" );
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document.write( "     In this way I will have a linear objective function  defined on the segment in the number line, and its minimum will be \r\n" );
document.write( "     at one of two endpoints of the segment.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Having this idea and the guiding instructions clearly formulated, can you, the student, complete this assignment on your own ?\r
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