document.write( "Question 818226: Use graphical methods to solve the following linear programming problem:\r
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Algebra.Com's Answer #492420 by AnlytcPhil(1806)\"\" \"About 
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document.write( "Maximize z=2x+4y\r\n" );
document.write( " subject to x+4y ≦ 18\r\n" );
document.write( " 4x+2y ≦ 16\r\n" );
document.write( " x ≧ 0\r\n" );
document.write( " y ≧ 0\r\n" );
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document.write( "We form the equations of graphs of the boundary lines\r\n" );
document.write( "lines by replacing the inequality symbols by equal \r\n" );
document.write( "signs.\r\n" );
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document.write( "x+4y = 18    <---line thru points (0,4.5) and (6,3) \r\n" );
document.write( "4x+2y = 16   <---line thru points (4,0) and (0,8)\r\n" );
document.write( "x = 0        <---the y-axis \r\n" );
document.write( "y = 0        <---the x-axis\r\n" );
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document.write( "We evaluate the objective function to maximize\r\n" );
document.write( "at each corner point:\r\n" );
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document.write( "Corner     z = 2x+4y\r\n" );
document.write( " (0,0)     z = 2(0)+4(0) = 0      <---- minimum value\r\n" );
document.write( " (0,4.5)   z = 2(0)+4(4.5) = 18\r\n" );
document.write( " (2,4)     z = 2(2)+4(4) = 20     <---- maximum value\r\n" );
document.write( " (4,0)     z = 2(4)+4(0) = 8\r\n" );
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document.write( "The maximum value of z is 20, and will occur at (2,4), when x=2 and y=4\r\n" );
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document.write( "Edwin
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