document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=745742>Question 745742</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need help with the following problem:<BR>\n" );
document.write( "A man and his daughter manufacture unfinished tables and chairs. Each table requires 3 hours of sawing and 1 hour of assembly. Each chair requires 2 hours of sawing and 2 hours of assembly. Between the two of them, they can put in up to 12 hours of sawing and 8 hours of assembly work each day. Find a system of inequalities that describes all possible combinations of tables and chairs that they can make daily. Graph the solution set.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #454004 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=454004\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A similar problem was posted a few days ago as problem number 743379.\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >= number of tables made per day<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" >= number of chairs made per day<BR>\n" );
document.write( "Two obvious constraints are<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3E=0 ALIGN=MIDDLE  ALT=\"x%3E=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%3E=0 ALIGN=MIDDLE  ALT=\"y%3E=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The amount of sawing to be done per day would be<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%2B2y%3C=12 ALIGN=MIDDLE  ALT=\"3x%2B2y%3C=12\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "The amount of assembling work to be done per day would be<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B2y%3C=8 ALIGN=MIDDLE  ALT=\"x%2B2y%3C=8\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "The inequalities above graph as a region of the x-y plane representing all the possible combinations of numbers of tables and chairs that they can make daily.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-1%2C9%2C-1%2C9%2C%0D%0Agrid%280%29%2C%0D%0Ablue%28line%280%2C6%2C4%2C0%29%29%2Cgreen%28line%280%2C4%2C8%2C0%29%29%2C%0D%0Alocate%284%2C0.5%2CC%29%2Clocate%280.1%2C0.5%2CO%29%2Clocate%28-0.5%2C4.2%2CA%29%2C%0D%0Alocate%282%2C3.5%2CB%29%2Clocate%280.1%2C6.5%2CD%29%2Clocate%288%2C0.5%2CE%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > The feasibility region is the quadrilateral OABC, bounded by the lines <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0 ALIGN=MIDDLE  ALT=\"x=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (the y-axis)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=0 ALIGN=MIDDLE  ALT=\"y=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (the x-axis)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%2B2y=12 ALIGN=MIDDLE  ALT=\"3x%2B2y=12\"   DISABLED_style= \"max-width:90%; height:auto;\" > (the blue line) and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B2y=8 ALIGN=MIDDLE  ALT=\"x%2B2y=8\"   DISABLED_style= \"max-width:90%; height:auto;\" > (the green line).<BR>\n" );
document.write( "To plot the blue and green line, I just found the x- and y-intercepts for each one.<BR>\n" );
document.write( "For <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%2B2y=12 ALIGN=MIDDLE  ALT=\"3x%2B2y=12\"   DISABLED_style= \"max-width:90%; height:auto;\" >:<BR>\n" );
document.write( "when <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0 ALIGN=MIDDLE  ALT=\"x=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2A0%2B2y=12 ALIGN=MIDDLE  ALT=\"3%2A0%2B2y=12\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2y=12 ALIGN=MIDDLE  ALT=\"2y=12\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=12%2F2 ALIGN=MIDDLE  ALT=\"y=12%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=6 ALIGN=MIDDLE  ALT=\"y=6\"   DISABLED_style= \"max-width:90%; height:auto;\" > gives us point D(0,6).<BR>\n" );
document.write( "When <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=0 ALIGN=MIDDLE  ALT=\"y=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%2B2%2A0=12 ALIGN=MIDDLE  ALT=\"3x%2B2%2A0=12\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x=12 ALIGN=MIDDLE  ALT=\"3x=12\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=12%2F3 ALIGN=MIDDLE  ALT=\"x=12%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=4 ALIGN=MIDDLE  ALT=\"x=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > gives us point C(4,0)<BR>\n" );
document.write( "For <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B2y=8 ALIGN=MIDDLE  ALT=\"x%2B2y=8\"   DISABLED_style= \"max-width:90%; height:auto;\" >:<BR>\n" );
document.write( "when <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0 ALIGN=MIDDLE  ALT=\"x=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0%2B2y=8 ALIGN=MIDDLE  ALT=\"0%2B2y=8\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2y=8 ALIGN=MIDDLE  ALT=\"2y=8\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=8%2F2 ALIGN=MIDDLE  ALT=\"y=8%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=4 ALIGN=MIDDLE  ALT=\"y=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > gives us point A(0,4).<BR>\n" );
document.write( "When <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=0 ALIGN=MIDDLE  ALT=\"y=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B2%2A0=8 ALIGN=MIDDLE  ALT=\"x%2B2%2A0=8\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=8 ALIGN=MIDDLE  ALT=\"x=8\"   DISABLED_style= \"max-width:90%; height:auto;\" > gives us point E(8,0).<BR>\n" );
document.write( "The intersection of the 2 lines is the point that satisfies <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%2B2y=12 ALIGN=MIDDLE  ALT=\"3x%2B2y=12\"   DISABLED_style= \"max-width:90%; height:auto;\" > and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B2y=8 ALIGN=MIDDLE  ALT=\"x%2B2y=8\"   DISABLED_style= \"max-width:90%; height:auto;\" >. It is the solution to<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%283x%2B2y=12%2Cx%2B2y=8%29 ALIGN=MIDDLE  ALT=\"system%283x%2B2y=12%2Cx%2B2y=8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x=12-8 ALIGN=MIDDLE  ALT=\"2x=12-8\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x=4 ALIGN=MIDDLE  ALT=\"2x=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=2 ALIGN=MIDDLE  ALT=\"x=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and<BR>\n" );
document.write( "with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28x=2%2Cx%2B2y=8%29 ALIGN=MIDDLE  ALT=\"system%28x=2%2Cx%2B2y=8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2B2y=8 ALIGN=MIDDLE  ALT=\"2%2B2y=8\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2y=8-2 ALIGN=MIDDLE  ALT=\"2y=8-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2y=6 ALIGN=MIDDLE  ALT=\"2y=6\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=3 ALIGN=MIDDLE  ALT=\"y=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "That intersection is the point C(2,3). </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );