document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1198987>Question 1198987</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve the linear programming programing by graphing and then determining which vertex maximizes the objective function  <BR>\n" );
document.write( "P=7x+9y<BR>\n" );
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document.write( "x+2y≤10<BR>\n" );
document.write( "4x+y≤12<BR>\n" );
document.write( "x≥0<BR>\n" );
document.write( "y≥0\r<BR>\n" );
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document.write( "What is the maximum value?  P = <BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #832664 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=832664\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> using the desmos.com calculator you would graph the opposite of the inequalities.<BR>\n" );
document.write( "the area on the graph that is not shaded is the region of feasibility.<BR>\n" );
document.write( "the corner points of the region is whaere the maximum value of P will be located.<BR>\n" );
document.write( "the corner points are:<BR>\n" );
document.write( "(0,5)<BR>\n" );
document.write( "(2,4)<BR>\n" );
document.write( "(3,0)<BR>\n" );
document.write( "the maximum value of P = 7x + 9y is located at (2,4) and the value of P at that point is 50.<BR>\n" );
document.write( "this is what the graph looks like.<BR>\n" );
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document.write( "all constraints need to be satisfied at that point.<BR>\n" );
document.write( "at the point (2,4):<BR>\n" );
document.write( "x+2y≤10 = 10 which is <= 10<BR>\n" );
document.write( "4x+y≤12 = 12 which is <= 12<BR>\n" );
document.write( "x and y are both >= 0\r<BR>\n" );
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