document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=221527>Question 221527</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can someone explain to me how to maximize by the simplex method?  I get confused after the second step.<BR>\n" );
document.write( "Here is the problem,<BR>\n" );
document.write( "Maximize P=0.3x ++ 0.4y<BR>\n" );
document.write( "Subject to: 4x + 8y equals or less than 1600<BR>\n" );
document.write( "            12x+8y equal or less than 1920<BR>\n" );
document.write( "            x equal to or greater than 0; y equal to or greater than 0<BR>\n" );
document.write( "Please help me.  I know how to do the first step of charting but the second step on confuses me?  How do I decide which negative should be the pivot point? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #166141 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=166141\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Here is the problem,<BR>\n" );
document.write( "Maximize P=0.3x ++ 0.4y<BR>\n" );
document.write( "Subject to: <BR>\n" );
document.write( "4x + 8y equals or less than 1600<BR>\n" );
document.write( "12x+8y equal or less than 1920<BR>\n" );
document.write( "x equal to or greater than 0; y equal to or greater than 0<BR>\n" );
document.write( "Please help me. I know how to do the first step of charting but the second step on confuses me? How do I decide which negative should be the pivot point?<BR>\n" );
document.write( "------------------------------------------<BR>\n" );
document.write( "Solve each of the inequalities for \"y\"<BR>\n" );
document.write( "y <=(-1/2)x + 200<BR>\n" );
document.write( "y <= (-3/2)x + 240<BR>\n" );
document.write( "---------------------------<BR>\n" );
document.write( "Plot those boundary lines and the intersecting solution regions.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C300%2C-10%2C50%2C-10%2C250%2Cy%3C=%28-1%2F2%29x%2B200%2Cy%3C=%28-3%2F2%29x%2B240%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "--------------------------<BR>\n" );
document.write( "Find the corners of the solution region:(0,0),(0,200),(40,180),(160.0)<BR>\n" );
document.write( "----------------------<BR>\n" );
document.write( "Check each of those number pairs in P=0.3x + 0.4y<BR>\n" );
document.write( "to determine which pair give you the maximum \"p\" value.<BR>\n" );
document.write( "(0,0) gives P = 0<BR>\n" );
document.write( "(0,200) gives p = 0 + 0.4*200 = 80<BR>\n" );
document.write( "(40,180) gives p = 0.3*40 + 0.4*180 = 84<BR>\n" );
document.write( "(150,0) gives p = 0.3*150 + 0 = 45<BR>\n" );
document.write( "--------------------------------------------<BR>\n" );
document.write( "So (40,180) gives the maximum Profit.<BR>\n" );
document.write( "===============================================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );