document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=468927>Question 468927</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do you do this problem?<BR>\n" );
document.write( "Minimize: Z = 6x+15y<BR>\n" );
document.write( "Subject to: 4x+5y>=27; 8x+4y>=32; x>=0;y>=0\r<BR>\n" );
document.write( "\n" );
document.write( "It's wanting to know the minimum value of Z and what point it occurs at. <BR>\n" );
document.write( "I can't figure out how to solve this. Thanks. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #321710 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=321710\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Minimize: Z = 6x+15y<BR>\n" );
document.write( "Subject to: 4x+5y>=27; 8x+4y>=32; x>=0;y>=0 <BR>\n" );
document.write( "----<BR>\n" );
document.write( "Graph each of the restraints:<BR>\n" );
document.write( "y >= (-4/5)x + (27/5)<BR>\n" );
document.write( "---<BR>\n" );
document.write( "y >= -2x +8<BR>\n" );
document.write( "---<BR>\n" );
document.write( "x >= 0 ; y >=0 means \"in the 1st quadrant\".<BR>\n" );
document.write( "----<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C-10%2C10%2C-10%2C10%2Cy+%3E=%28-4%2F5%29x%2B%2827%2F5%29%2Cy%3E=-2x%2B8%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-------------<BR>\n" );
document.write( "Notice the enclosed area in the 1st quadrant.<BR>\n" );
document.write( "---<BR>\n" );
document.write( "Find the coordinates of the vertices of the enclosed area:<BR>\n" );
document.write( "(0,5.4),(4,0), (2 1/6,3 2/3)<BR>\n" );
document.write( "----<BR>\n" );
document.write( "Objective Function: Minimize: Z = 6x+15y<BR>\n" );
document.write( "----<BR>\n" );
document.write( "Evaluate the objective function at each of the<BR>\n" );
document.write( "vertex values.<BR>\n" );
document.write( "Example:<BR>\n" );
document.write( "Using (0,5.4) you would get z = (6*0)+(15*4) = 60<BR>\n" );
document.write( "Using (2 1/6, 2 2/3) you would get z = (6*13/6)+15(8/3) = 13+40 = 53<BR>\n" );
document.write( "etc.<BR>\n" );
document.write( "===============<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( "================= </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );