document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=322796>Question 322796</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve the following Linear Programming problem using the corner point method.\r<BR>\n" );
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document.write( "      Maximize -   3X + 5Y<BR>\n" );
document.write( "      Subject to -<BR>\n" );
document.write( "                   4X + 4y <=48<BR>\n" );
document.write( "                    X + 2Y <=20<BR>\n" );
document.write( "                    X,Y >= o\r<BR>\n" );
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document.write( "   a) Plot the graph for each<BR>\n" );
document.write( "   b)  Find the four corner points<BR>\n" );
document.write( "   c)  Find the profit for each Point<BR>\n" );
document.write( "   d)  What is the maximum profit?\r<BR>\n" );
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document.write( "My answer:<BR>\n" );
document.write( "  Graph 4x + 4y <= 48       Graph x + 2y = 20<BR>\n" );
document.write( "      X= 0 y=12                  x= 0  y= 10 <BR>\n" );
document.write( "      x= 0 y= 12                 x = 20 y= 0\r<BR>\n" );
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document.write( "I have done the graph but I do not know how to work the rest\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #231649 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=231649\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Solve the following Linear Programming problem using the corner point method. <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28x%2Cy%29=3x+%2B+5y ALIGN=MIDDLE  ALT=\"P%28x%2Cy%29=3x+%2B+5y\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-2%2C12%2C-2%2C12%2Cgrid%281%29%2Ccircle%280%2C0%2C.3%29%2Ccircle%2812%2C0%2C.3%29%2Ccircle%280%2C10%2C0.3%29%2Ccircle%284%2C8%2C0.3%29%2C%0D%0Ablue%28line%284%2C8%2C0%2C10%29%29%2C%0D%0Ablue%28line%284%2C8%2C12%2C0%29%29%2C%0D%0Ablue%28line%280%2C10%2C0%2C0%29%29%2C%0D%0Ablue%28line%2812%2C0%2C0%2C0%29%29%2C%0D%0Ablue%28line%280.1%2C0.1%2C0.1%2C10%29%29%2C%0D%0Ablue%28line%280.1%2C0.1%2C12%2C0.1%29%29%2C%0D%0Agreen%28line%28-10%2C22%2C4%2C8%29%29%2C%0D%0Agreen%28line%2815%2C-3%2C12%2C0%29%29%2C%0D%0Ared%28line%28-10%2C15%2C0%2C10%29%29%2C%0D%0Ared%28line%284%2C8%2C16%2C2%29%29%2C%0D%0Agraph%28300%2C300%2C-2%2C12%2C-2%2C12%2C0%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The feasible region (shown by the blue polygon) is formed from the two lines and the two axes. The intersection of the lines with the axes give two points, the intersection of the axes (0,0) gives a third point. <BR>\n" );
document.write( "You also need to find the intersection of the two lines to get the fourth point in the feasible region:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=12-x ALIGN=MIDDLE  ALT=\"y=12-x\"   DISABLED_style= \"max-width:90%; height:auto;\" > and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%2820-x%29%2F2 ALIGN=MIDDLE  ALT=\"y=%2820-x%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "which occurs at (4,8).<BR>\n" );
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document.write( "c)The maximum and minimum for P(x,y) occurs at one of the vertices.<BR>\n" );
document.write( "Calculate the value at each of them,<BR>\n" );
document.write( "(<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=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >):<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P=3x%2B5y=0 ALIGN=MIDDLE  ALT=\"P=3x%2B5y=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(<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=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >):<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P=3x%2B5y=3%2812%29=36 ALIGN=MIDDLE  ALT=\"P=3x%2B5y=3%2812%29=36\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(<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=10 ALIGN=MIDDLE  ALT=\"10\"   DISABLED_style= \"max-width:90%; height:auto;\" >):<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P=3x%2B5y=5%2810%29=50 ALIGN=MIDDLE  ALT=\"P=3x%2B5y=5%2810%29=50\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(<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=8 ALIGN=MIDDLE  ALT=\"8\"   DISABLED_style= \"max-width:90%; height:auto;\" >):<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P=3x%2B5y=3%284%29%2B5%288%29=52 ALIGN=MIDDLE  ALT=\"P=3x%2B5y=3%284%29%2B5%288%29=52\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "d)The maximum profit of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=52 ALIGN=MIDDLE  ALT=\"52\"   DISABLED_style= \"max-width:90%; height:auto;\" > occurs when <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;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=8 ALIGN=MIDDLE  ALT=\"y=8\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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