document.write( "Question 548268: Maximization
\n" ); document.write( "Maximize p = 7x - 4y subject to
\n" ); document.write( "y >= 2x - 8
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\n" ); document.write( "y <= (x + 8) / 2
\n" ); document.write( "x >= 1
\n" ); document.write( "y >= 2\r
\n" ); document.write( "\n" ); document.write( "Thank you \n" ); document.write( "

Algebra.Com's Answer #356870 by Edwin McCravy(20056) $\"\"$ $\"About$

You can put this solution on YOUR website!
The other tutor apparently didn't understand what you want.
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document.write( "We draw the lines\r\n" );
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document.write( "y=2x-8, y=10-x, y=, x=1, and y=2 \r\n" );
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document.write( "Maximization \r\n" );
document.write( "Maximize p = 7x - 4y subject to\r\n" );
document.write( "y ≧ 2x - 8,  the red line y=2x-8 and the region above it, since it's y≧\r\n" );
document.write( "y ≦ 10 - x, the green line y=10-x and the region below it, since it's y≦\r\n" );
document.write( "y ≦ , the blue line y= and the region below it, since it's y≦\r\n" );
document.write( "x ≧ 1, the black line x=1 and the region to the right of it, since it's x≧\r\n" );
document.write( "y ≧ 2, the purple line y=2 and the region above it, since it's y≧\r\n" );
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document.write( "We will chop off the unnecessary parts of the lines, leaving \r\n" );
document.write( "only the region bounded by them, which is this pentagon:\r\n" );
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document.write( "Now we must find all the corner points of this pentagon, by solving these\r\n" );
document.write( "five systems:\r\n" );
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document.write( " the red and green lines, which gives (6,4)\r\n" );
document.write( " the red and purple lines, which gives (5,2)\r\n" );
document.write( " the black and purple lines, which gives (1,2)\r\n" );
document.write( " the blue and black lines, which gives (1,4.5).\r\n" );
document.write( " the blue and green lines, which gives (4,6)\r\n" );
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document.write( "We evaluate p = 7x - 4y at each of those corner points:\r\n" );
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document.write( "Corner point | p = 7x - 4y\r\n" );
document.write( "    (1,2)    |     -1\r\n" );
document.write( "    (5,2)    |     27\r\n" );
document.write( "    (6,4)    |     26\r\n" );
document.write( "    (4,6)    |      4\r\n" );
document.write( "  (1,4.5)    |    -11\r\n" );
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document.write( "So the maximum value of p=27 occurs when x=5 and y=2\r\n" );
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document.write( "Edwin

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