document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=884657>Question 884657</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the minimum and maximum values of the objective function subject to the given constraints.<BR>\n" );
document.write( "Objective Function: C=4x+3y<BR>\n" );
document.write( "Constraints: x is greater than or equal to 0<BR>\n" );
document.write( "             2x + 3y is greater than or equal to 6<BR>\n" );
document.write( "             3x - 2y is less than or equal to 9<BR>\n" );
document.write( "             x + 5y is less than or equal to 20<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #534577 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=534577\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> First find the feasible region and vertices.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2B3y%3E=6 ALIGN=MIDDLE  ALT=\"2x%2B3y%3E=6\"   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%2C8%2C-2%2C8%2Cy%3E=%286-2x%29%2F3%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C-2%2C8%2C-2%2C8%2Cy%3E=%286-2x%29%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x-2y%3C=9 ALIGN=MIDDLE  ALT=\"3x-2y%3C=9\"   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%2C8%2C-2%2C8%2Cy%3E=%283x-9%29%2F2%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C-2%2C8%2C-2%2C8%2Cy%3E=%283x-9%29%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B5y%3C=20 ALIGN=MIDDLE  ALT=\"x%2B5y%3C=20\"   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%2C8%2C-2%2C8%2Cy%3C=%2820-x%29%2F5%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C-2%2C8%2C-2%2C8%2Cy%3C=%2820-x%29%2F5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( ".\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-2%2C8%2C-2%2C8%2Cgrid%281%29%2Ccircle%280%2C2%2C0.2%29%2Ccircle%280%2C4%2C0.2%29%2Ccircle%283%2C0%2C0.2%29%2Ccircle%285%2C3%2C0.2%29%2C%0D%0Ablue%28line%280%2C2%2C0%2C4%29%29%2C%0D%0Ablue%28line%280%2C4%2C5%2C3%29%29%2C%0D%0Ablue%28line%285%2C3%2C3%2C0%29%29%2C%0D%0Ablue%28line%283%2C0%2C0%2C2%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The vertices here were easy to find graphically but you could have solved for them algebraically also.<BR>\n" );
document.write( "The extrema occur at the vertices.<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".\r<BR>\n" );
document.write( "\n" );
document.write( "(0,2):<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C=4%280%29%2B3%282%29=highlight%286%29 ALIGN=MIDDLE  ALT=\"C=4%280%29%2B3%282%29=highlight%286%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(0,4):<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C=4%280%29%2B3%284%29=12 ALIGN=MIDDLE  ALT=\"C=4%280%29%2B3%284%29=12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(5,3):<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C=4%285%29%2B3%283%29=highlight%2829%29 ALIGN=MIDDLE  ALT=\"C=4%285%29%2B3%283%29=highlight%2829%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(3,0):<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C=4%283%29%2B3%280%29=12 ALIGN=MIDDLE  ALT=\"C=4%283%29%2B3%280%29=12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );