document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=892441>Question 892441</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What are the maximum and minimum values of objective function p=x+4y with given restraints x-y<=4 , x<=2, 0<=y<=5 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #540556 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=540556\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> First graph the feasible region.<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-6%2C6%2C-6%2C6%2Cgrid%281%29%2Cblue%28line%282%2C-20%2C2%2C20%29%29%2Ccircle%282%2C5%2C0.2%29%2Ccircle%282%2C0%2C0.2%29%2Cblue%28line%28-10%2C5%2C10%2C5%29%29%2Cgraph%28300%2C300%2C-6%2C6%2C-6%2C6%2Cx-4%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The feasible region is simplified to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3C=2 ALIGN=MIDDLE  ALT=\"x%3C=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0%3C=y%3C=5 ALIGN=MIDDLE  ALT=\"0%3C=y%3C=5\"   DISABLED_style= \"max-width:90%; height:auto;\" > and the line <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-y%3C=4 ALIGN=MIDDLE  ALT=\"x-y%3C=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > does not contribute any constraint. <BR>\n" );
document.write( "Since there is no minimum value for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >, there is no minimum value for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p ALIGN=MIDDLE  ALT=\"p\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "The maximum value occurs at one of the two vertices.<BR>\n" );
document.write( "(2,0):<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=2%2B4%280%29=2 ALIGN=MIDDLE  ALT=\"p=2%2B4%280%29=2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2,5):<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=2%2B4%285%29=2%2B20=22 ALIGN=MIDDLE  ALT=\"p=2%2B4%285%29=2%2B20=22\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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