document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=145904>Question 145904</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0132191415/algebrahomeworkh>Blitzer College Algebra</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> z=2x+4y<BR>\n" );
document.write( "x>=0, y>=0  Linear programming problem, graphing a solution, and maximum.<BR>\n" );
document.write( "x+3y>=6<BR>\n" );
document.write( "x+y>=3<BR>\n" );
document.write( "x+y<=9\r<BR>\n" );
document.write( "\n" );
document.write( "I come up with serveral vertices.  Even when using the example.  I know how to put the vertices back into the equations, but I need to figure out how to limit or pick the correct vertices;  (0,0), (0,2), (6,0), (0,3), (3,0), (5,4), (6,3), (0,9)  My graphe looks like a octagon kind of including 0.  I am missing something and trying desperately to understand this.  Can someone show me how I conclude which vertices are correct?\r<BR>\n" );
document.write( "\n" );
document.write( "Heidi </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #106481 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=106481\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> z=2x+4y<BR>\n" );
document.write( "x>=0, y>=0 Linear programming problem, graphing a solution, and maximum.<BR>\n" );
document.write( "x+3y>=6<BR>\n" );
document.write( "x+y>=3<BR>\n" );
document.write( "x+y<=9 <BR>\n" );
document.write( "I come up with serveral vertices. Even when using the example. I know how to put the vertices back into the equations, but I need to figure out how to limit or pick the correct vertices; (0,0), (0,2), (6,0), (0,3), (3,0), (5,4), (6,3), (0,9) <BR>\n" );
document.write( "--------------<BR>\n" );
document.write( "(0,0),(0,2),(3,0),(5,4) and (6,3) are not vertices of the <BR>\n" );
document.write( "area that is enclose by y>=-x+3, y>=(-1/3)x+2, and y<=-3+9.<BR>\n" );
document.write( "------------<BR>\n" );
document.write( "Notice that two of the inequalities are above their boundary lines<BR>\n" );
document.write( "and the 3rd is below it boundary line.<BR>\n" );
document.write( "-------------<BR>\n" );
document.write( "The vertices you want are (6,0),(9,0),(0,3),(0,9), and (3/2,3/2)<BR>\n" );
document.write( "-------------<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C300%2C-10%2C10%2C-10%2C10%2C%28-1%2F3%29x%2B2%2C-x%2B3%2C-x%2B9%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C300%2C-10%2C10%2C-10%2C10%2C%28-1%2F3%29x%2B2%2C-x%2B3%2C-x%2B9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );