Algebra.Com's Answer #183440 by Edwin McCravy(20056)![\"\"](\"/images/stars/stars-13.gif\")  
You can put this solution on YOUR website!
Maximize z = 2x + 4y subject to the constraints\r
\n" );
document.write( "\n" );
document.write( "x ≥ 0, y ≥ 0, x + y ≥ 1, 3x + 2y <= 6\r
\n" );
document.write( "\n" );
document.write( "\r\n" );
document.write( " \r\n" );
document.write( "When x is \"greater than\" it means \"to the right of\".\r\n" );
document.write( "That means that the feasible region is on or to\r\n" );
document.write( "the right of the line whose equation is  which\r\n" );
document.write( "is the line which is the y-axis.\r\n" );
document.write( "\r\n" );
document.write( " \r\n" );
document.write( "When y is \"greater than\" it means \"above\"\r\n" );
document.write( "That means that the feasible region is on or \r\n" );
document.write( "above the line whose equation is  which\r\n" );
document.write( "is the line which is the x-axis.\r\n" );
document.write( "\r\n" );
document.write( "Those two mean the feasible region is in this upper right-\r\n" );
document.write( "hand part of the xy-coordinate system:\r\n" );
document.write( "\r\n" );
document.write( " \r\n" );
document.write( "\r\n" );
document.write( " \r\n" );
document.write( "If you solve that for x you get  \r\n" );
document.write( "When x is \"greater than\" it means \"to the right of\"\r\n" );
document.write( "If you solve that for y you get  \r\n" );
document.write( "When y is \"greater than\" it means \"above\".\r\n" );
document.write( "That means that the feasible region is on or \r\n" );
document.write( "above and to the right of the line whose equation is\r\n" );
document.write( " . The x-intercept of that line is (1,0),\r\n" );
document.write( "and the y-intercept is (0,1). \r\n" );
document.write( "\r\n" );
document.write( "That's above and to the\r\n" );
document.write( "right of the green line below, and of course right of\r\n" );
document.write( "the y-axis and above the x-axis:\r\n" );
document.write( "\r\n" );
document.write( " \r\n" );
document.write( "\r\n" );
document.write( " \r\n" );
document.write( "If you solve that for x you get  \r\n" );
document.write( "When x is \"less than\" it means \"to the left of\"\r\n" );
document.write( "If you solve that for y you get  \r\n" );
document.write( "When y is \"less than\" it means \"below\".\r\n" );
document.write( "That means that the feasible region is on or \r\n" );
document.write( "bolow and to the left of the line whose equation is\r\n" );
document.write( " . The x-intercept of that line is (2,0),\r\n" );
document.write( "and the y-intercept is (0,3). That's below and to the \r\n" );
document.write( "left of the blue line below, and of course right of the \r\n" );
document.write( "y-axis and above the x-axis, and above and to the right \r\n" );
document.write( "of the green line:\r\n" );
document.write( " \r\n" );
document.write( "\r\n" );
document.write( "The corner points of that region are (1,0), (2,0), (0,3), and (0,1)\r\n" );
document.write( "So we list them in this table with the objective function evaluated\r\n" );
document.write( "at each corner point:\r\n" );
document.write( "\r\n" );
document.write( " \r\n" );
document.write( "\r\n" );
document.write( "Corner point | Value of z = 2x+4y\r\n" );
document.write( "----------------|--------------------------- \r\n" );
document.write( " (1,0) | z = 2(1)+4(0) = 2+0 = 2\r\n" );
document.write( " |\r\n" );
document.write( " (2,0) | z = 2(2)+4(0) = 4+0 = 4 \r\n" );
document.write( " |\r\n" );
document.write( " (0,3) | z = 2(0)+4(3) = 0+12 = 12\r\n" );
document.write( " |\r\n" );
document.write( " (0,1) | z = 2(0)+4(1) = 0+4 = 4\r\n" );
document.write( "\r\n" );
document.write( " \r\n" );
document.write( "The instructions were to maximize the objective function.\r\n" );
document.write( "So we see that the maximum value of the objective\r\n" );
document.write( "function is 12 when x=0 and y=3.\r\n" );
document.write( "\r\n" );
document.write( "[Note: If the problem had asked us to minimize\r\n" );
document.write( "the objective function. the answer would have been that the minimum\r\n" );
document.write( "value of the objective function would be 2 when x=1 and y=0.]\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Edwin \r
\n" );
document.write( "
\n" );
document.write( "\n" );
document.write( " \n" );
document.write( " |