document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=91307>Question 91307</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello. I'm having problems with maximums in linear programming. <BR>\n" );
document.write( "What is the maximum value of z=3x+y for the region given by the system:<BR>\n" );
document.write( "x>= 0<BR>\n" );
document.write( "y>= 0<BR>\n" );
document.write( "1/2x+y<=11<BR>\n" );
document.write( "3x+2y<= 30\r<BR>\n" );
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document.write( "I'm sure you have to plot a graph and find the feasible region. I just can't remember how to plot the graph correctly. \r<BR>\n" );
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document.write( "Thanks so much. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #66286 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=66286\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> What is the maximum value of z=3x+y for the region given by the system:<BR>\n" );
document.write( "x>= 0<BR>\n" );
document.write( "y>= 0<BR>\n" );
document.write( "These two conditions limit the search to the 1st Quadrant.<BR>\n" );
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document.write( "1/2x+y<=11<BR>\n" );
document.write( "Solve for y so you can graph this restriction:<BR>\n" );
document.write( "y <= (-1/2)x + 11<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C300%2C-10%2C25%2C-10%2C25%2C%28-1%2F2%29x+%2B+11%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C300%2C-10%2C25%2C-10%2C25%2C%28-1%2F2%29x+%2B+11%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "---------------<BR>\n" );
document.write( "Find the coordinates of the intersection points of the <BR>\n" );
document.write( "restricion lines.<BR>\n" );
document.write( "Put those coordinate vales into the objective function, z=3x+y,<BR>\n" );
document.write( "and see which coordinate pair give a maximum value.<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
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