document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=530477>Question 530477</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the minimum and maximum values of the objective function subject to the given constrants.   Objective function:  C= 2x + 3y<BR>\n" );
document.write( "                    Constraints:<BR>\n" );
document.write( "x>0<BR>\n" );
document.write( "y>0<BR>\n" );
document.write( "x +y < 9\r<BR>\n" );
document.write( "\n" );
document.write( "I also have to graph this and I just don't get how to even start this type of a problem. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #350062 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=350062\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Find the minimum and maximum values of the objective function subject to the given constrants. Objective function: C= 2x + 3y<BR>\n" );
document.write( "Constraints:<BR>\n" );
document.write( "x>0<BR>\n" );
document.write( "y>0<BR>\n" );
document.write( "Comment: These two conditions tell you the answers are in the 1st Quadrant.<BR>\n" );
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document.write( "x +y < 9<BR>\n" );
document.write( "Graph the boundary line: y = -x+9<BR>\n" );
document.write( "Solutions points are below the boundary line and in the 1st Quadrant.<BR>\n" );
document.write( "---<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C-10%2C10%2C-10%2C10%2C-x%2B9%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C400%2C-10%2C10%2C-10%2C10%2C-x%2B9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "====<BR>\n" );
document.write( "The vertices you need to check are (0,0),(0,9),(9,0)<BR>\n" );
document.write( "(0,0): 2*0+3*0 = 0 (minimum)<BR>\n" );
document.write( "(0,9): 2*0+3*9 = 27 (maximum)<BR>\n" );
document.write( "(9,0): 2*9+3*0 = 18<BR>\n" );
document.write( "========================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( " </SPAN>\n" );
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