document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=176633>Question 176633</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Which point gives the minimum value for P = 3x + 2y and lies within<BR>\n" );
document.write( "the system of restrictions?\r<BR>\n" );
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document.write( "( < all of them are equal or greater than but i just dont kno how to do that on here)\r<BR>\n" );
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document.write( "1 < x < 6<BR>\n" );
document.write( "2 < y < 5<BR>\n" );
document.write( "x + y < 10\r<BR>\n" );
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document.write( "A. (1, 2) B. (0, 0) C. (5, 5) D. (1, 5) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #131894 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=131894\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> First find the feasible region and vertices.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1+%3C=+x+%3C=+6 ALIGN=MIDDLE  ALT=\"1+%3C=+x+%3C=+6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2+%3C=+y+%3C=+5 ALIGN=MIDDLE  ALT=\"2+%3C=+y+%3C=+5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The last one involves a little more work.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By%3C=10 ALIGN=MIDDLE  ALT=\"x%2By%3C=10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%3C=-x%2B10 ALIGN=MIDDLE  ALT=\"y%3C=-x%2B10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Let's graph the line and the other boundaries<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28+300%2C+300%2C+-1%2C+11%2C+-1%2C+11%2Cgrid%28+1+%29%2Ccircle%28+0%2C+0%2C+.2+%29%2C%0D%0Agreen%28line%28-2%2C2%2C12%2C2%29%29%2C%0D%0Agreen%28line%28-2%2C5%2C12%2C5%29%29%2C%0D%0Agreen%28line%281%2C-1%2C1%2C15%29%29%2C%0D%0Agreen%28line%286%2C-1%2C6%2C15%29%29%2C%0D%0Agraph%28+300%2C+300%2C+-1%2C+11%2C+-1%2C+11%2C+-x%2B10%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The feasible region is then, <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28+300%2C+300%2C+-1%2C+7%2C+-1%2C+7%2Cgrid%28+1+%29%2C%0D%0Acircle%28+1%2C+2%2C+.2+%29%2C%0D%0Acircle%28+1%2C+5%2C+.2+%29%2C%0D%0Acircle%28+6%2C+2%2C+.2+%29%2C%0D%0Acircle%28+6%2C+4%2C+.2+%29%2C%0D%0Acircle%28+5%2C+5%2C+.2+%29%2C%0D%0A%0D%0Agreen%28line%281%2C2%2C6%2C2%29%29%2C%0D%0Agreen%28line%281%2C2%2C1%2C5%29%29%2C%0D%0Agreen%28line%285%2C5%2C6%2C4%29%29%2C%0D%0Agreen%28line%286%2C2%2C6%2C4%29%29%2C%0D%0Agreen%28line%286%2C4%2C5%2C5%29%29%2C%0D%0Agreen%28line%285%2C5%2C1%2C5%29%29%0D%0A%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The vertices are then<BR>\n" );
document.write( "(1,2)<BR>\n" );
document.write( "(1,5)<BR>\n" );
document.write( "(6,2)<BR>\n" );
document.write( "(6,4)<BR>\n" );
document.write( "(5,5)<BR>\n" );
document.write( "The corresponding values of P are<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%281%2C2%29=3%281%29+%2B+2%282%29=7 ALIGN=MIDDLE  ALT=\"P%281%2C2%29=3%281%29+%2B+2%282%29=7\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%281%2C5%29=3%281%29+%2B+2%285%29=13 ALIGN=MIDDLE  ALT=\"P%281%2C5%29=3%281%29+%2B+2%285%29=13\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%286%2C2%29=3%286%29+%2B+2%282%29=22 ALIGN=MIDDLE  ALT=\"P%286%2C2%29=3%286%29+%2B+2%282%29=22\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%286%2C4%29=3%286%29+%2B+2%284%29=26 ALIGN=MIDDLE  ALT=\"P%286%2C4%29=3%286%29+%2B+2%284%29=26\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%285%2C5%29=3%285%29+%2B+2%285%29=22 ALIGN=MIDDLE  ALT=\"P%285%2C5%29=3%285%29+%2B+2%285%29=22\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The minimum value for P of 7 occurs at (1,2).<BR>\n" );
document.write( "The correct answer is A. </SPAN>\n" );
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