document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1202520>Question 1202520</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Maximize z=4x+5y\r<BR>\n" );
document.write( "\n" );
document.write( "subject to<BR>\n" );
document.write( "x+y\le 4<BR>\n" );
document.write( "x-y\ge -2<BR>\n" );
document.write( "x\le 3<BR>\n" );
document.write( "x\ge 0<BR>\n" );
document.write( "y\ge 0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #837407 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=837407\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Plot the five inequalities shown using graphing software such as Desmos or GeoGebra. <BR>\n" );
document.write( "The overlapped shaded region is a quadrilateral with these five corner points<BR>\n" );
document.write( "(0,0)<BR>\n" );
document.write( "(0,2)<BR>\n" );
document.write( "(1,3)<BR>\n" );
document.write( "(3,1)<BR>\n" );
document.write( "(3,0)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Test each corner point with the objective function to see which gives the largest value of z.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Testing (0,0)<BR>\n" );
document.write( "z=4x+5y<BR>\n" );
document.write( "z=4*0+5*0<BR>\n" );
document.write( "z=0\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Now try (0,2)<BR>\n" );
document.write( "z=4x+5y<BR>\n" );
document.write( "z=4*0+5*2<BR>\n" );
document.write( "z=10<BR>\n" );
document.write( "This result is larger than the previous.<BR>\n" );
document.write( "So far (0,2) yields the largest z value.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Now try (1,3)<BR>\n" );
document.write( "z=4x+5y<BR>\n" );
document.write( "z=4*1+5*3<BR>\n" );
document.write( "z=19<BR>\n" );
document.write( "This result is larger than the previous.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Now try (3,1)<BR>\n" );
document.write( "z=4x+5y<BR>\n" );
document.write( "z=4*3+5*1<BR>\n" );
document.write( "z=17<BR>\n" );
document.write( "This result is NOT larger than the previous. So we ignore this.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Lastly we need to try (3,0)<BR>\n" );
document.write( "z=4x+5y<BR>\n" );
document.write( "z=4*3+5*0<BR>\n" );
document.write( "z=12<BR>\n" );
document.write( "This result is NOT larger than 19, so we ignore this.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Answer: <BR>\n" );
document.write( "The max value is z = 19.<BR>\n" );
document.write( "It occurs when (x,y) = (1,3)<BR>\n" );
document.write( "</font> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );