document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1029073>Question 1029073</A>: <I><SPAN STYLE=\"word-break: break-all;\"> List the maximum and minimum for the following system of equations.<BR>\n" );
document.write( "x is greater than or equal to 0<BR>\n" );
document.write( "y is greater than or equal to 0<BR>\n" );
document.write( "y is smaller than or equal to x+10<BR>\n" );
document.write( "y is smaller than or equal to 2x+1<BR>\n" );
document.write( "f(x)=x-2y </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #644161 by </B><A HREF=/tutors/aboutme.mpl?userid=robertb><B>robertb(5830)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=robertb><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=robertb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=644161\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The feasibility region is an unbounded region with the following corner points:\r<BR>\n" );
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document.write( "(0,0), (1, 19), and (0,1).\r<BR>\n" );
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document.write( "By the fundamental theorem of linear programming, the max and min are among these corner points.\r<BR>\n" );
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document.write( "At (0,0), f = 0-2*0 = 0<BR>\n" );
document.write( "At (1, 19), f = 1 - 2*-19 = -37<BR>\n" );
document.write( "At  (0,1), f = 0 - 2*1 = -2\r<BR>\n" );
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document.write( "Therefore the maximum value is 0 and the minimum value is -37.<BR>\n" );
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