document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1102103>Question 1102103</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I have no idea how to calculate this. Appreciate the help. Thanks.<BR>\n" );
document.write( "Solve the following linear programming problem.<BR>\n" );
document.write( "Minimize: z=5x+30y<BR>\n" );
document.write( "subject to: 9x+12y&#8805;61<BR>\n" );
document.write( "                  8x+4y&#8805;32<BR>\n" );
document.write( " x&#8805;&#8203;0, y&#8805;0<BR>\n" );
document.write( "What is the minimum value of z?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #716786 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=716786\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  I have no idea how to calculate this. Appreciate the help. Thanks.<BR>\n" );
document.write( "Solve the following linear programming problem.<BR>\n" );
document.write( "Minimize: z=5x+30y<BR>\n" );
document.write( "subject to: <BR>\n" );
document.write( "9x+12y&#8805;61<BR>\n" );
document.write( "8x+4y&#8805;32<BR>\n" );
document.write( "x&#8805;&#8203;0, y&#8805;0<BR>\n" );
document.write( "What is the minimum value of z?<BR>\n" );
document.write( "---------------<BR>\n" );
document.write( "x >= 0 and y >= 0 means the answers are in the 1st quadrant<BR>\n" );
document.write( "Solve the two other inequalities for \"y\"::<BR>\n" );
document.write( "y >= (-3/4)x + (61/12)<BR>\n" );
document.write( "y >= (-2)x + 8<BR>\n" );
document.write( "--------------------<BR>\n" );
document.write( "Plot those lines in Quadrant I<BR>\n" );
document.write( "The y-intersects are (0,61/12) and (0,8)<BR>\n" );
document.write( "The x-intersects are ([(61/12)/(3/4)],0) and (4,0)<BR>\n" );
document.write( "---<BR>\n" );
document.write( "Find the intersection of the two inequalities<BR>\n" );
document.write( "(-3/4)x+(61/12) = -2x+8<BR>\n" );
document.write( "(5/4)x = 3/4<BR>\n" );
document.write( "x = 3/5<BR>\n" );
document.write( "Then y = -2(3/5)+8 = 34/5<BR>\n" );
document.write( "That vertex is (3/5,34/5)<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "Find the 4 vertex polygon in Quadrant I including (0,0)<BR>\n" );
document.write( "Vertices:: (0,0) ; (0,5) ; (4,0) ; (7/3,10/3)<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "Check for z in z = 5x+30y for each of the (x,y) pairs<BR>\n" );
document.write( "(0,0):: z = 5*0+30*0 = 0<BR>\n" );
document.write( "(0,5):: z = 5*0+30*5 = 150<BR>\n" );
document.write( "(4,0):: z = 5*4+30*0 = 20<BR>\n" );
document.write( "(7/3,10/3):: z = 5(7/3)+30(10/3) = [35+300]/3 = 112 when rounded<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "Ans:: Minimum z is zero<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( "--------------- </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );