document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=323823>Question 323823</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the minimum and maximum values of z=2x+3y if possible, for the following set of constraints\r<BR>\n" );
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document.write( "x+y&#8804;9<BR>\n" );
document.write( "-x+y&#8804;5<BR>\n" );
document.write( "2x-y&#8804;14\r<BR>\n" );
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document.write( "Find minimum value & maximum value.\r<BR>\n" );
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document.write( "Please help! :)  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #231794 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=231794\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> First find the feasible region using the constraints.<BR>\n" );
document.write( "Find the intersection points.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9-x=5%2Bx ALIGN=MIDDLE  ALT=\"9-x=5%2Bx\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x=4 ALIGN=MIDDLE  ALT=\"2x=4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=2 ALIGN=MIDDLE  ALT=\"x=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=7 ALIGN=MIDDLE  ALT=\"y=7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2,7)<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9-x=2x%2B14 ALIGN=MIDDLE  ALT=\"9-x=2x%2B14\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x=-5 ALIGN=MIDDLE  ALT=\"3x=-5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-5%2F3 ALIGN=MIDDLE  ALT=\"x=-5%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=9-%28-5%2F3%29=32%2F3 ALIGN=MIDDLE  ALT=\"y=9-%28-5%2F3%29=32%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(-5/3,32/3)<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2B14=5%2Bx ALIGN=MIDDLE  ALT=\"2x%2B14=5%2Bx\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-9 ALIGN=MIDDLE  ALT=\"x=-9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=5-9=-4 ALIGN=MIDDLE  ALT=\"y=5-9=-4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(-9,-4)<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-10%2C10%2C-5%2C15%2Cgrid%281%29%2C+circle%28-9%2C-4%2C.4%29%2Ccircle%28-5%2F3%2C32%2F3%2C0.4%29%2Ccircle%282%2C7%2C0.4%29%2Cgraph%28300%2C300%2C-10%2C10%2C-5%2C15%2C9-x%2C5%2Bx%2C2x%2B14%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
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document.write( "The min and max of the function will occur at one of the vertices:<BR>\n" );
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document.write( "(2,7):<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z=2x%2B3y=2%282%29%2B3%287%29=25 ALIGN=MIDDLE  ALT=\"z=2x%2B3y=2%282%29%2B3%287%29=25\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(-5/3,32/3):<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z=2x%2B3y=2%28-5%2F3%29%2B3%2832%2F3%29=86%2F3 ALIGN=MIDDLE  ALT=\"z=2x%2B3y=2%28-5%2F3%29%2B3%2832%2F3%29=86%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(-9,-4):<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z=2x%2B3y=2%28-9%29%2B3%28-4%29=-30 ALIGN=MIDDLE  ALT=\"z=2x%2B3y=2%28-9%29%2B3%28-4%29=-30\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "The min value of z of -30 occurs at (-9,-4).<BR>\n" );
document.write( "The max value of z of 86/3 occurs at (-5/3,32/3). </SPAN>\n" );
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