document.write( "Question 1202520: Maximize z=4x+5y\r
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\n" ); document.write( "x+y\le 4
\n" ); document.write( "x-y\ge -2
\n" ); document.write( "x\le 3
\n" ); document.write( "x\ge 0
\n" ); document.write( "y\ge 0 \n" ); document.write( "

Algebra.Com's Answer #837410 by Edwin McCravy(20056) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "Did you mean ? I suppose so.\r\n" );
document.write( "Multiply it through by -1 and change\r\n" );
document.write( "the direction of the inequality.\r\n" );
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document.write( "The last two inequalities means we are in the first quadrant.\r\n" );
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document.write( "So we draw the three boundary lines, which are just like the inequalities, \r\n" );
document.write( "except we replace the symbol of inequality with an \" = \".  \r\n" );
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document.write( "So we draw  in red, green, blue, and purple\r\n" );
document.write( "respectively\r\n" );
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document.write( "Pick the origin (x,y) = (0,0) x=0, y=0 as a test point in the inequality for\r\n" );
document.write( "each of the boundary lines to determine whether the shading is above or below\r\n" );
document.write( "a slanted or horizontal boundary line or right or left or a vertical bountary line.\r\n" );
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document.write( "Substitute x=0, y=0 in ,  get  which is true, so the\r\n" );
document.write( "origin is a solution, and is below the line, so all solutions are on or below\r\n" );
document.write( "the line x+y=4.  So we are to shade below the line x+y=4.\r\n" );
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document.write( "Substitute x=0, y=0 in ,  get  which is true, so the\r\n" );
document.write( "origin is a solution, and is below the line, so all solutions are on or below\r\n" );
document.write( "the line -x+y=2.  So we are to shade below the line x+y=4.\r\n" );
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document.write( "Substitute x=0, y=0 in ,  get  which is true, so the\r\n" );
document.write( "origin is a solution, and is left of the line, so all solutions are on or left\r\n" );
document.write( "of the line x=3.  So we are to shade left the line x=3.\r\n" );
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document.write( "So we are to shade the region which is below all three lines. So\r\n" );
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document.write( "There are 5 corner points in the shaded region: \r\n" );
document.write( "(0,0), (0,2), (1,3), (3,1), (3,0)\r\n" );
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document.write( "The maximum and minimum values of z=4x+5y will be at one of these:\r\n" );
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document.write( "Evaluating z=4x+5y at (0,0) gives z = 4(0)+5(0) = 0+0 = 0.\r\n" );
document.write( "Evaluating z=4x+5y at (0,2) gives z = 4(0)+5(2) = 0+10 = 10\r\n" );
document.write( "Evaluating z=4x+5y at (1,3) gives z = 4(1)+5(3) = 4+15 = 19.\r\n" );
document.write( "Evaluating z=4x+5y at (3,1) gives z = 4(3)+5(1) = 12+5 = 17\r\n" );
document.write( "Evaluating z=4x+5y at (3,0) gives z = 4(3)+5(0) =12+0 = 12.\r\n" );
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document.write( "So it turns out that the maximum value of z is 19 when x=1 and y=3.\r\n" );
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document.write( "Edwin

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