document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=787508>Question 787508</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the minimum and maximum values of the objective function subject to the given constraints.<BR>\n" );
document.write( "Objective function:<BR>\n" );
document.write( "C=2x+5y<BR>\n" );
document.write( "Constraints:<BR>\n" );
document.write( "x is less than or equal to 5<BR>\n" );
document.write( "y is greater than or equal to 4<BR>\n" );
document.write( "-2x+5y is less than or equal to 30 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #478222 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39617)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=478222\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> What we would do is first graph these descriptions onto x y plane:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3C=5 ALIGN=MIDDLE  ALT=\"x%3C=5\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%3E=4 ALIGN=MIDDLE  ALT=\"y%3E=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2x%2B5y%3C=30 ALIGN=MIDDLE  ALT=\"-2x%2B5y%3C=30\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "That will form a planar figure.  You would expect the optimal solution to C to be one of the vertices of this planar figure.  Test each vertex point, and find which one give the maximum and which gives the minimum.\r<BR>\n" );
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document.write( "The first two constraints are simple to graph.  The last given constraint may be easiest as slope-intercept form: 5y<=2x+30, into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%3C=%282%2F5%29x%2B6 ALIGN=MIDDLE  ALT=\"y%3C=%282%2F5%29x%2B6\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "You would continue with this graph to pick your vertex points:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C-7%2C7%2C-1%2C9%2C4%2C%282%2F5%29x%2B6%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C-7%2C7%2C-1%2C9%2C4%2C%282%2F5%29x%2B6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >UNFORTUNATELY, entering x<=5 will not work in this rendering method, so it NEEDS to be included, but is missing.\r<BR>\n" );
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document.write( "Points to check will be (-5,4), (5,4), and  (5,8). </SPAN>\n" );
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