document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1162552>Question 1162552</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Minimize P subject to the following constraints.<BR>\n" );
document.write( "P = 9y + x<BR>\n" );
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document.write( "x ≥ 0<BR>\n" );
document.write( "y ≥ 0<BR>\n" );
document.write( "x + y ≥ 3<BR>\n" );
document.write( "2y − x ≤ 1\r<BR>\n" );
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document.write( "Find the minimum value of P. <BR>\n" );
document.write( "P=\r<BR>\n" );
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document.write( "&\r<BR>\n" );
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document.write( "Find the point where the minimum occurs. <BR>\n" );
document.write( "(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 #786368 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13219)</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=786368\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "Constraint boundary lines:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+-x%2B3 ALIGN=MIDDLE  ALT=\"y+=+-x%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%281%2F2%29x%2B%281%2F2%29 ALIGN=MIDDLE  ALT=\"y+=+%281%2F2%29x%2B%281%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Intersection point: (5/3,4/3)<br><BR>\n" );
document.write( "a graph... feasibility region is above the red line and below the green line<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C-1%2C5%2C-1%2C5%2C-x%2B3%2C.5x%2B.5%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C400%2C-1%2C5%2C-1%2C5%2C-x%2B3%2C.5x%2B.5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The only two corners of the feasibility region are (3,0) and (5/3,4/3).<br><BR>\n" );
document.write( "(3,0): P = 9(0)+3 = 3<BR>\n" );
document.write( "(5/3,4/3): P = 9(4/3)+5/3 = 41/3<br><BR>\n" );
document.write( "ANSWERS: The minimum value of P is 3, at the point (3,0).<br><BR>\n" );
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