document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1162582>Question 1162582</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Minimize  P = y − x  subject to the following constraints.<BR>\n" );
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document.write( "x ≥ 0<BR>\n" );
document.write( "y ≥ 0<BR>\n" );
document.write( "x + y ≤ 9<BR>\n" );
document.write( "2x + y ≥ 2\r<BR>\n" );
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document.write( "minimum value. P =<BR>\n" );
document.write( "point where minimum occurs. (x, y) = </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #786400 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13203)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=786400\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The constraint boundary lines are<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+-x%2B9 ALIGN=MIDDLE  ALT=\"y+=+-x%2B9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+-2x%2B2 ALIGN=MIDDLE  ALT=\"y+=+-2x%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "A graph; the feasibility region is below the red line and above the green....<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C-2%2C10%2C-2%2C10%2C-x%2B9%2C-2x%2B2%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C400%2C-2%2C10%2C-2%2C10%2C-x%2B9%2C-2x%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The objective function is not very realistic; it is obvious that P = y-x will have its minimum value where y is smallest and x is largest -- at (9,0).<br><BR>\n" );
document.write( "But to practice the standard method for solving this kind of problem, you can evaluate the objective function at all four corner points -- (1,0), (9,0), (0,2), and (0,9).<br><BR>\n" );
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