document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=85541>Question 85541</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need help understanding how to solve these types of problems: I've looked at many examples but i do not see it.\r<BR>\n" );
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document.write( "Use the simplex method to solve the linear programming problem:\r<BR>\n" );
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document.write( "minimize: W= 4y1+2y2<BR>\n" );
document.write( "Subject to:<BR>\n" );
document.write( "3y1+2y2>=60<BR>\n" );
document.write( "4y1+y2>=40<BR>\n" );
document.write( "y1>=0,y2>=0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #61823 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=61823\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Use the simplex method to solve the linear programming problem: <BR>\n" );
document.write( "minimize: W= 4y1+2y2<BR>\n" );
document.write( "Subject to:<BR>\n" );
document.write( "3y1+2y2>=60<BR>\n" );
document.write( "4y1+y2>=40<BR>\n" );
document.write( "y1>=0,y2>=0<BR>\n" );
document.write( "--------------<BR>\n" );
document.write( "Draw a y1-y2 coordinate system; let y2 be the horizontal axis.<BR>\n" );
document.write( "Graph y1 >=(-2/3)y2+20\r<BR>\n" );
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document.write( "Graph y1 >=(-1/4)y2+10<BR>\n" );
document.write( "Graph y1>=0<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C300%2C-5%2C40%2C-5%2C30%2C%28-2%2F3%29x%2B20%2C%28-1%2F4%29x%2B10%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C300%2C-5%2C40%2C-5%2C30%2C%28-2%2F3%29x%2B20%2C%28-1%2F4%29x%2B10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Graph y2>=0<BR>\n" );
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document.write( "Find all the intersection points of the EQUALITY statements.<BR>\n" );
document.write( "These are (0,10), (0,20) and (24,4)<BR>\n" );
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document.write( "Evaluate w = 4y1 + 2y2 for each of the intersection coordinate pairs.<BR>\n" );
document.write( "For (0,10) you get w = 20<BR>\n" );
document.write( "For (0,20) you get w = 40<BR>\n" );
document.write( "For (24,4) you get 4*24+2*4 = 104<BR>\n" );
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document.write( "Select the coordinate pair that gives you the minimum w value as your solution<BR>\n" );
document.write( "That would be y1=0, y2=10.<BR>\n" );
document.write( "==============<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H. <BR>\n" );
document.write( "  </SPAN>\n" );
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