document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=346507>Question 346507</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A furniture manufacturer can make from 30 to 60 tables a day and from 40 to 100 chairs a day.  It can make at most 120 units in one day. The profit on a table is $150, and the profit on a chair is $65. How many tables and chairs should they make per day to maximize profit.  How much is the maximum profit? \r<BR>\n" );
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document.write( "P= 150x + 65 y<BR>\n" );
document.write( "30 <= x <= 60<BR>\n" );
document.write( "40 <= y <= 100<BR>\n" );
document.write( "x + y <= 120<BR>\n" );
document.write( "x => 0<BR>\n" );
document.write( "y => 0\r<BR>\n" );
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document.write( "Graph your system of inequalities<BR>\n" );
document.write( "Label the vertices and find their coordinates </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #247846 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=247846\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Determine the vertices.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=30 ALIGN=MIDDLE  ALT=\"x=30\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=40 ALIGN=MIDDLE  ALT=\"y=40\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(30,40)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=60 ALIGN=MIDDLE  ALT=\"x=60\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=40 ALIGN=MIDDLE  ALT=\"y=40\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(60,40)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By=120 ALIGN=MIDDLE  ALT=\"x%2By=120\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=30%2By=120 ALIGN=MIDDLE  ALT=\"30%2By=120\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=90 ALIGN=MIDDLE  ALT=\"y=90\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(30,90)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By=120 ALIGN=MIDDLE  ALT=\"x%2By=120\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60%2By=120 ALIGN=MIDDLE  ALT=\"60%2By=120\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=60 ALIGN=MIDDLE  ALT=\"y=60\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(60,60)<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-10%2C90%2C-5%2C95%2C%0D%0Agrid%281%29%2C%0D%0Ablue%28line%2830%2C-100%2C30%2C200%29%29%2C%0D%0Ablue%28line%2860%2C-100%2C60%2C200%29%29%2C%0D%0Agreen%28line%28-100%2C100%2C200%2C100%29%29%2C%0D%0Agreen%28line%28-100%2C40%2C200%2C40%29%29%2C%0D%0Acircle%2830%2C40%2C1.8%29%2C%0D%0A%0D%0Acircle%2860%2C40%2C1.8%29%2C%0D%0Acircle%2860%2C60%2C1.8%29%2C%0D%0Acircle%2830%2C90%2C1.8%29%2C%0D%0Agraph%28300%2C300%2C-10%2C90%2C-5%2C95%2C120-x%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "The maximum (and minimum) values occur(s) at the vertices.<BR>\n" );
document.write( "(30,40):<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P=+150x+%2B+65y=150%2830%29%2B65%2840%29=7100 ALIGN=MIDDLE  ALT=\"P=+150x+%2B+65y=150%2830%29%2B65%2840%29=7100\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(60,40):<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P=+150x+%2B+65y=150%2860%29%2B65%2840%29=11600 ALIGN=MIDDLE  ALT=\"P=+150x+%2B+65y=150%2860%29%2B65%2840%29=11600\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(30,90):<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P=+150x+%2B+65y=150%2830%29%2B65%2890%29=10350 ALIGN=MIDDLE  ALT=\"P=+150x+%2B+65y=150%2830%29%2B65%2890%29=10350\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(60,60):<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28P=+150x+%2B+65y=150%2860%29%2B65%2860%29=12900%29 ALIGN=MIDDLE  ALT=\"highlight%28P=+150x+%2B+65y=150%2860%29%2B65%2860%29=12900%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Make 60 of each to maximize profits.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );