document.write( "Question 926184: Maximize:
\n" ); document.write( "C = 3x + 4y
\n" ); document.write( "Constraints:
\n" ); document.write( "x + y ≤ 10
\n" ); document.write( "– x + y ≤ 5
\n" ); document.write( "2x + 4y ≤ 32 \n" ); document.write( "

Algebra.Com's Answer #562800 by Fombitz(32388) $\"\"$ $\"About$

You can put this solution on YOUR website!
First, map out the feasible region.
\n" ); document.write( " $\"x%2By%3C=10\"$
\n" ); document.write( " $\"y%3C=-x%2B10\"$
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\n" ); document.write( " $\"graph%28300%2C300%2C-3%2C12%2C-3%2C12%2C-x%2B10%29\"$
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\n" ); document.write( ".
\n" ); document.write( " $\"graph%28300%2C300%2C-3%2C12%2C-3%2C12%2Cy%3C=-x%2B10%29\"$
\n" ); document.write( ".
\n" ); document.write( ".
\n" ); document.write( " $\"-x+%2B+y+%3C=5\"$
\n" ); document.write( " $\"y%3C=x%2B5\"$
\n" ); document.write( ".
\n" ); document.write( ".
\n" ); document.write( ".
\n" ); document.write( " $\"graph%28300%2C300%2C-3%2C12%2C-3%2C12%2C-x%2B10%2Cx%2B5%29\"$
\n" ); document.write( ".
\n" ); document.write( ".\r
\n" ); document.write( "\n" ); document.write( " $\"2x%2B4y%3C=32\"$
\n" ); document.write( " $\"x%2B2y%3C=16\"$
\n" ); document.write( " $\"2y%3C=-x%2B16\"$
\n" ); document.write( " $\"y%3C=-x%2F2%2B8\"$
\n" ); document.write( ".
\n" ); document.write( ".
\n" ); document.write( ".
\n" ); document.write( " $\"graph%28300%2C300%2C-3%2C12%2C-3%2C12%2C-x%2B10%2Cx%2B5%2C-x%2F2%2B8%29\"$
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\n" ); document.write( "Find the vertices of the intersection points.
\n" ); document.write( " $\"-x%2F2%2B8=x%2B5\"$
\n" ); document.write( " $\"-x%2B16=2x%2B10\"$
\n" ); document.write( " $\"3x=6\"$
\n" ); document.write( " $\"x=2\"$
\n" ); document.write( "Then,
\n" ); document.write( " $\"y=2%2B5\"$
\n" ); document.write( " $\"y=7\"$
\n" ); document.write( "(2,7)
\n" ); document.write( "and
\n" ); document.write( " $\"-x%2F2%2B8=-x%2B10\"$
\n" ); document.write( " $\"-x%2B16=-2x%2B20\"$
\n" ); document.write( " $\"x=4\"$
\n" ); document.write( "Then,
\n" ); document.write( " $\"y=-4%2B10\"$
\n" ); document.write( " $\"y=6\"$
\n" ); document.write( "(4,6)
\n" ); document.write( "Also include,
\n" ); document.write( "(0,5) and (10,0).
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\n" ); document.write( "Now check the function using these points:
\n" ); document.write( "(2,7)
\n" ); document.write( " $\"C+=+3x+%2B+4y=3%282%29%2B4%287%29=6%2B28=34\"$
\n" ); document.write( "(4,6)
\n" ); document.write( " $\"C+=+3x+%2B+4y=3%284%29%2B4%286%29=12%2B24=36\"$
\n" ); document.write( "(0,5)
\n" ); document.write( " $\"C+=+3x+%2B+4y=3%280%29%2B4%285%29=0%2B20=20\"$
\n" ); document.write( "(10,0)
\n" ); document.write( " $\"C+=+3x+%2B+4y=3%2810%29%2B4%280%29=30%2B0=30\"$
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\n" ); document.write( "The maximum occurs at (2,7) \n" ); document.write( "

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