document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1152458>Question 1152458</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Consider the feasible region in the xy-plane defined by the following linear inequalities.<BR>\n" );
document.write( "x ≥ 0<BR>\n" );
document.write( "y ≥ 0<BR>\n" );
document.write( "x ≤ 12<BR>\n" );
document.write( "x + y ≥ 4<BR>\n" );
document.write( "-x + 2y ≤ 14\r<BR>\n" );
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document.write( "1. Find the coordinates of the vertices of the feasible region. Clearly show how each vertex is<BR>\n" );
document.write( "determined and which lines form the vertex.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #774530 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=774530\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <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;\" ><BR>\n" );
document.write( "<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( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%3C=+12 ALIGN=MIDDLE  ALT=\"x+%3C=+12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%2B+y+%3E=+4 ALIGN=MIDDLE  ALT=\"x+%2B+y+%3E=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x+%2B+2y+%3C=+14 ALIGN=MIDDLE  ALT=\"-x+%2B+2y+%3C=+14\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
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document.write( "intersection of these two lines:<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;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%2B+y++%3E=+4 ALIGN=MIDDLE  ALT=\"x+%2B+y++%3E=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+%2B+y++%3E=+4 ALIGN=MIDDLE  ALT=\"0+%2B+y++%3E=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y++%3E=+4 ALIGN=MIDDLE  ALT=\"y++%3E=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "first vertices: at  (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "intersection of these two lines:<BR>\n" );
document.write( "<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( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x+%2B+2y+%3C=+14 ALIGN=MIDDLE  ALT=\"-x+%2B+2y+%3C=+14\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x+%2B+2%2A0+%3C=+14 ALIGN=MIDDLE  ALT=\"-x+%2B+2%2A0+%3C=+14\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3E=14 ALIGN=MIDDLE  ALT=\"x%3E=14\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "second vertices: at  (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=14 ALIGN=MIDDLE  ALT=\"14\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "intersection of these two lines:\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3C=+12 ALIGN=MIDDLE  ALT=\"x%3C=+12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x+%2B+2y+%3C=+14 ALIGN=MIDDLE  ALT=\"-x+%2B+2y+%3C=+14\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-12+%2B+2y+%3C=14 ALIGN=MIDDLE  ALT=\"-12+%2B+2y+%3C=14\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2y+%3C=+14%2B12 ALIGN=MIDDLE  ALT=\"2y+%3C=+14%2B12\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2y+%3C=+26 ALIGN=MIDDLE  ALT=\"2y+%3C=+26\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+%3C=+13 ALIGN=MIDDLE  ALT=\"y+%3C=+13\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "third vertices: at  (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12 ALIGN=MIDDLE  ALT=\"12\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=13 ALIGN=MIDDLE  ALT=\"13\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "intersection of these two lines:\r<BR>\n" );
document.write( "\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;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x+%2B+2y+%3C=+14 ALIGN=MIDDLE  ALT=\"-x+%2B+2y+%3C=+14\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-0%2B+2y+%3C=+14 ALIGN=MIDDLE  ALT=\"-0%2B+2y+%3C=+14\"   DISABLED_style= \"max-width:90%; height:auto;\" >=> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2y+%3C=+14 ALIGN=MIDDLE  ALT=\"+2y+%3C=+14\"   DISABLED_style= \"max-width:90%; height:auto;\" >=>  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+%3C=+7 ALIGN=MIDDLE  ALT=\"y+%3C=+7\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "fourth vertices: at  (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7 ALIGN=MIDDLE  ALT=\"7\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "intersection of these two lines:<BR>\n" );
document.write( "<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( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%2B+y+%3E=+4 ALIGN=MIDDLE  ALT=\"x+%2B+y+%3E=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3E=4 ALIGN=MIDDLE  ALT=\"x%3E=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "fifth vertices: at  (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
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document.write( "sketch:\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF=\"https://www.imageupload.net/image/Jbb7g\"><IMG STYLE=\"max-width:80%;\" src=\"https://www.imageupload.net/upload-image/2020/02/15/MSP1.th.gif\" alt=\"MSP1.gif\" border=\"0\" /></a>\r<BR>\n" );
document.write( "<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28+600%2C+600%2C+-15%2C+20%2C+-15%2C+20%2C%0D%0Acircle%280%2C7%2C.2%29%2Ccircle%2812%2C13%2C.2%29%2Ccircle%2812%2C0%2C.2%29%2Ccircle%280%2C4%2C.2%29%2Ccircle%284%2C0%2C.2%29%2C%0D%0Agreen%28line%280%2C4%2C0%2C7%29%29%2Cgreen%28line%280%2C4%2C4%2C0%29%29%2Cgreen%28line%2812%2C0%2C4%2C0%29%29%2Cgreen%28line%2812%2C0%2C12%2C13%29%29%2Cgreen%28line%280%2C7%2C12%2C13%29%29%2Clocate%283.5%2C5%2Cthe-feasible-region%29%2C%0D%0Alocate%280%2C7.2%2Cv%280%2C7%29%29%2Clocate%280%2C4.2%2Cv%280%2C4%29%29%2Clocate%284%2C-0.6%2Cv%284%2C0%29%29%2Clocate%2812%2C-0.6%2Cv%2812%2C0%29%29%2C+locate%2812%2C13%2Cv%2812%2C13%29%29%2C%0D%0A%0D%0A%0D%0A+graph%28+600%2C+600%2C+-15%2C+20%2C+-15%2C+20%2C+0%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );