document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=251014>Question 251014</A>: <I><SPAN STYLE=\"word-break: break-all;\"> find the maximum value of the objective function z=3x+5y subject to the folloing constraints: x greater than or equal to 2, y greater than or equal to 0, x+y less than or equal to 6. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #182828 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=182828\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Graph the constraints to find the feasible region.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3E=2 ALIGN=MIDDLE  ALT=\"x%3E=2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%3E=0 ALIGN=MIDDLE  ALT=\"y%3E=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By%3C=6 ALIGN=MIDDLE  ALT=\"x%2By%3C=6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%3C=6-x ALIGN=MIDDLE  ALT=\"y%3C=6-x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28+300%2C+300%2C+-2%2C+8%2C+-2%2C+8%2Cgrid%28+1+%29%2Ccircle%28+2%2C+0%2C+.2+%29%2C%0D%0Acircle%286%2C0%2C0.2%29%2C%0D%0Agreen%28line%286%2C0.1%2C2%2C0.1%29%29%2C%0D%0Agreen%28line%282%2C0%2C2%2C4%29%29%2C%0D%0Agreen%28line%282.05%2C4.05%2C6.05%2C0.05%29%29%2C%0D%0Acircle%282%2C4%2C0.2%29%2Cgraph%28+300%2C+300%2C+-2%2C+8%2C+-2%2C8%2C+6-x%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "As we see the feasible region is a triangle with vertices at (2,0),(2,4),and (0,6).<BR>\n" );
document.write( "The max and min of the objective function occurs at one of these vertices.<BR>\n" );
document.write( "(2,0): <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+z=3x%2B5y=3%282%29%2B5%280%29=6 ALIGN=MIDDLE  ALT=\"+z=3x%2B5y=3%282%29%2B5%280%29=6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2,4): <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+z=3x%2B5y=3%282%29%2B5%284%29=26 ALIGN=MIDDLE  ALT=\"+z=3x%2B5y=3%282%29%2B5%284%29=26\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(6,0): <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+z=3x%2B5y=3%286%29%2B5%280%29=18 ALIGN=MIDDLE  ALT=\"+z=3x%2B5y=3%286%29%2B5%280%29=18\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The max value of 26 occurs at (2,4).  </SPAN>\n" );
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