document.write( "Question 1207825: use graphical methods and the corner point theorem to maximize z=x+5y subject to 3x+2y<12
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Algebra.Com's Answer #845954 by mccravyedwin(408)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "What Greenestamps means is this:\r\n" );
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document.write( "The objective function z=x+5y can be written in slope intercept form y=mx+b\r\n" );
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document.write( "\"y=expr%28-1%2F5%29x%2Bz\" where -1/5 is the slope, and z is the y intercept.  \r\n" );
document.write( "Think of all the parallel lines that have slope -1/5. \r\n" );
document.write( "I'll draw a bunch of them across my graph:\r\n" );
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document.write( "You see that the only two of those parallel lines that intersect the feasible\r\n" );
document.write( "region in only one corner points are the ones with y-intercept 6 and 0.\r\n" );
document.write( "So the maximum value of z is 6 (when x=0, y=6) and the minimum value of z \r\n" );
document.write( "is 0 (when x=0, y=0).  Many times you can just visualize mentally how steep,\r\n" );
document.write( "or how non-steep, the objective function slants, whether it slants upward\r\n" );
document.write( "or downward and determine by inspection which are the points at which the\r\n" );
document.write( "maximum and minimum values of z occur without substituting the corner points in\r\n" );
document.write( "the objective function.   \r\n" );
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document.write( "But be aware that it won't always be the top and bottom ones like it is in this\r\n" );
document.write( "particular example.  The shapes of feasible regions differ greatly. \r\n" );
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document.write( "Edwin

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