document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=856331>Question 856331</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the ordered pair where the maximum value occurs for the equation C=12x-4y given the following constraints:\r<BR>\n" );
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document.write( "y>-(greater than or equal to)4<BR>\n" );
document.write( "x>-(greater than or equal to )1<BR>\n" );
document.write( "x+2y<-(less than or equal to)16<BR>\n" );
document.write( "y-x<-(less than or equal to) 5\r<BR>\n" );
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document.write( "A)(10,1)<BR>\n" );
document.write( "B(8,4)<BR>\n" );
document.write( "C(2,7)<BR>\n" );
document.write( "D)(1,4) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #516010 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=516010\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Just as a note, <= is less than or equal and >= is greater t<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B2y%3C=16 ALIGN=MIDDLE  ALT=\"x%2B2y%3C=16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C-2%2C10%2C-2%2C10%2Cy%3C=%2816-x%29%2F2%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C-2%2C10%2C-2%2C10%2Cy%3C=%2816-x%29%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-x%3C=5 ALIGN=MIDDLE  ALT=\"y-x%3C=5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C-2%2C10%2C-2%2C10%2Cy%3C=x%2B5%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C-2%2C10%2C-2%2C10%2Cy%3C=x%2B5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "First graph the region.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-2%2C10%2C-2%2C10%2C%0D%0Agreen%28line%28-20%2C4%2C20%2C4%29%29%2C%0D%0Agreen%28line%281%2C-20%2C1%2C20%29%29%2C%0D%0Agraph%28300%2C300%2C-2%2C10%2C-2%2C10%2C%2816-x%29%2F2%2Cx%2B5%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Find the points of intersection.<BR>\n" );
document.write( "(1,4)<BR>\n" );
document.write( "(1,6)<BR>\n" );
document.write( "(2,7)<BR>\n" );
document.write( "(8,4)<BR>\n" );
document.write( "First graph the region.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-2%2C10%2C-2%2C10%2C%0D%0Acircle%281%2C4%2C0.2%29%2C%0D%0Acircle%281%2C6%2C0.2%29%2C%0D%0Acircle%282%2C7%2C0.2%29%2C%0D%0Acircle%288%2C4%2C0.2%29%2C%0D%0Agreen%28line%28-20%2C4%2C20%2C4%29%29%2C%0D%0Agreen%28line%281%2C-20%2C1%2C20%29%29%2C%0D%0Agraph%28300%2C300%2C-2%2C10%2C-2%2C10%2C%2816-x%29%2F2%2Cx%2B5%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The min and max values occur at one of these vertices.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C=12x-4y=12%281%29-4%284%29=12-16=-4 ALIGN=MIDDLE  ALT=\"C=12x-4y=12%281%29-4%284%29=12-16=-4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C=12x-4y=12%281%29-4%286%29=12-24=-12 ALIGN=MIDDLE  ALT=\"C=12x-4y=12%281%29-4%286%29=12-24=-12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C=12x-4y=12%282%29-4%287%29=24-28=-4 ALIGN=MIDDLE  ALT=\"C=12x-4y=12%282%29-4%287%29=24-28=-4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C=12x-4y=12%288%29-4%284%29=96-16=80 ALIGN=MIDDLE  ALT=\"C=12x-4y=12%288%29-4%284%29=96-16=80\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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