document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=163239>Question 163239</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How would you find the maximum and minimum values, if they exist, of the objective function for the given constraints?:\r<BR>\n" );
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document.write( "P=5y+3x<BR>\n" );
document.write( "Constraints:<BR>\n" );
document.write( "x+y<6<BR>\n" );
document.write( "x-y<4<BR>\n" );
document.write( "x>0<BR>\n" );
document.write( "y>0\r<BR>\n" );
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document.write( "Thank you!!! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #120319 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=120319\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> When you plot you constraints, your feasible region is triangular patch with vertices at (4,0),(6,0),and (5,1). <BR>\n" );
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document.write( "The min and max values will occur at the vertices. <BR>\n" );
document.write( "P(4,0)=5(0)+3(4)=12<BR>\n" );
document.write( "P(6,0)=5(0)+3(6)=18<BR>\n" );
document.write( "P(5,1)=5(1)+3(5)=20<BR>\n" );
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document.write( "Min value of P=12 and occurs at (4,0).<BR>\n" );
document.write( "Max value of P=20 and occurs at (5,1).<BR>\n" );
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document.write( "Since the inequalities do not include the lines (\">\" and \"<\" and not \"<=\" and \">=\", these values for P are limits for P and are not obtained in the feasible region.<BR>\n" );
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