document.write( "Question 84764This question is from textbook finite mathmatics
\n" ); document.write( ": The maximum value of z = 5x + 4y subject to \r
\n" ); document.write( "\n" ); document.write( "3x + y < 24
\n" ); document.write( "6x + 4y < 66
\n" ); document.write( "x > 0, y > 0 is \r
\n" ); document.write( "\n" ); document.write( "A. 96
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\n" ); document.write( "C. 56
\n" ); document.write( "D. 40 \n" ); document.write( "
Algebra.Com's Answer #61054 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "The maximum value of z = 5x + 4y subject to \r\n" );
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document.write( "3x + y < 24\r\n" );
document.write( "6x + 4y < 66\r\n" );
document.write( "x > 0, y > 0 is \r\n" );
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document.write( "A. 96\r\n" );
document.write( "B. 66\r\n" );
document.write( "C. 56\r\n" );
document.write( "D. 40\r\n" );
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document.write( "Graph the boundary lines:\r\n" );
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document.write( "1.     3x + y = 24  (3x + y < 24 will \r\n" );
document.write( "be the region on or below this line)\r\n" );
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document.write( "2.     6x + 4y = 66  (6x + 4y < 66 will \r\n" );
document.write( "be the region on or below this line)\r\n" );
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document.write( "3.     x = 0  (x > 0 will be the \r\n" );
document.write( "region on or to the right of this line, \r\n" );
document.write( "which is just the y-axis.\r\n" );
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document.write( "  \r\n" );
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document.write( "4.     y = 0  (y > 0 will be the \r\n" );
document.write( "region on or above this line, which is \r\n" );
document.write( "just the x-axis.\r\n" );
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document.write( "You can shade the common region.  I can't shade \r\n" );
document.write( "on here so I will just erase all the parts of \r\n" );
document.write( "the lines that I don't need:\r\n" );
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document.write( "Now we will find all four corner points.\r\n" );
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document.write( "The top point is found by solving the system\r\n" );
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document.write( "6x + 4y = 66\r\n" );
document.write( "x = 0\r\n" );
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document.write( "That has the solution (0,16.5)\r\n" );
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document.write( "The bottom left point is obviously the \r\n" );
document.write( "origin but is found by solving the system\r\n" );
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document.write( "x = 0\r\n" );
document.write( "y = 0\r\n" );
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document.write( "That has solution (0,0)\r\n" );
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document.write( "The bottom right point is found by solving\r\n" );
document.write( "the system\r\n" );
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document.write( "3x + y = 24\r\n" );
document.write( "y = 0 \r\n" );
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document.write( "That has solution (8,0)\r\n" );
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document.write( "The point in the middle is found by solving \r\n" );
document.write( "the system\r\n" );
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document.write( "3x + y = 24\r\n" );
document.write( "6x + 4y = 66\r\n" );
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document.write( "That has solution (5,9)\r\n" );
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document.write( "Now both the maximum and the minimum values of\r\n" );
document.write( "the objective function \r\n" );
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document.write( "z = 5x + 4y\r\n" );
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document.write( "will occur at corner points. So we make this table:\r\n" );
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document.write( "corner point |  x  |  y  |    z = 5x + 4y   |\r\n" );
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document.write( "   (0,16.5)  |  0  |16.5 |  5(0)+4(16.5)=66   \r\n" );
document.write( "    (0,0)    |  0  |  0  |  5(0)+4(0) =   0\r\n" );
document.write( "    (8,0)    |  8  |  0  |  5(8)+4(0) =  40\r\n" );
document.write( "    (5,9)    |  5  |  9  |  5(5)+4(9) =  61\r\n" );
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document.write( "So we find that the maximum value of the\r\n" );
document.write( "objective function z is 66 when x=0 and y=16.5\r\n" );
document.write( "(and the minimum value is 0 when x=0 and y=0).\r\n" );
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document.write( "But you wanted the maximum value so it's\r\n" );
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document.write( "z = 66 when x=0 and y = 16.5, which is\r\n" );
document.write( "choice B.\r\n" );
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document.write( "Edwin

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