document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1118359>Question 1118359</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me to understand how to do \"optimization\"\r<BR>\n" );
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document.write( "Objective function: C = 8x+10y Maximize<BR>\n" );
document.write( "Constraints<BR>\n" );
document.write( "2x+y _< 12<BR>\n" );
document.write( "x+3y _< 21\r<BR>\n" );
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document.write( "X_>0, y_>0\r<BR>\n" );
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document.write( "Then I need to graph it?<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 #733638 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=733638\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Objective function: C = 8x+10y Maximize<BR>\n" );
document.write( "Constraints<BR>\n" );
document.write( "2x+y _< 12<BR>\n" );
document.write( "x+3y _< 21 <BR>\n" );
document.write( "X_>0, y_>0 <BR>\n" );
document.write( "Graph this first, it will be easier to understand<BR>\n" );
document.write( "We need the 1st two equations to be changed to the slope intercept<BR>\n" );
document.write( "2x + y = 12<BR>\n" );
document.write( "y = -2x + 12<BR>\n" );
document.write( "and<BR>\n" );
document.write( "x + 3y = 21<BR>\n" );
document.write( "3y = -x + 21<BR>\n" );
document.write( "y = -<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F3 ALIGN=MIDDLE  ALT=\"1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >x + 7<BR>\n" );
document.write( "Graph these equations, the area of interest is below the lowest line<BR>\n" );
document.write( "Note that only positive solutions are considered<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-4%2C+10%2C+-4%2C+14%2C+-2x%2B12%2C+-%281%2F3%29x%2B7%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+200%2C+-4%2C+10%2C+-4%2C+14%2C+-2x%2B12%2C+-%281%2F3%29x%2B7%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Find the objective solution at the point of intersection which is 3,6<BR>\n" );
document.write( "C = 8x + 10y<BR>\n" );
document.write( "C = 8(3) + 10(6)<BR>\n" );
document.write( "C = 24 + 60<BR>\n" );
document.write( "C = 84<BR>\n" );
document.write( "Find the other two objective solutions<BR>\n" );
document.write( "x=0, y=7<BR>\n" );
document.write( "C = 8(0) + 10(7)<BR>\n" );
document.write( "C = 70<BR>\n" );
document.write( "and<BR>\n" );
document.write( "x=6, y=0<BR>\n" );
document.write( "C = 8(6) + 10(0)<BR>\n" );
document.write( "C = 48<BR>\n" );
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document.write( "Obviously the optimum (max) objective solution is x=3, y=6, which is 84 \r<BR>\n" );
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