document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1131186>Question 1131186</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do I find the values of x and y that produce the maximum ad minimum in the objective function if c=4x + 5y?<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #747812 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52805)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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/cgi-bin/show-face.mpl?user=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=747812\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "When solving a minimax problem with a linear objective function by the method of Linear programming,\r\n" );
document.write( "\r\n" );
document.write( "you should determine a feasible domain first.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Usually, in 2D problems (as in your problem with c = 4x + 5y), it is a polygon.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "In the most simple version of the LP-method (which student usually learn first), the algorithm is to calculate the values\r\n" );
document.write( "\r\n" );
document.write( "of the objective function at the corners of the feasibility polygon, and then to select that vertex (corner),\r\n" );
document.write( "\r\n" );
document.write( "where the objective function has minimal / (maximal) value.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "To calculate the value of the objective function  c = 4x + 5y at a vertex, simply substitute the coordinate values \r\n" );
document.write( "of the vertex into the function's expression.\r\n" );
document.write( "</PRE>\r<BR>\n" );
document.write( "\n" );
document.write( "---------------\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "To see concrete minimax problems solved by the Linear Programming method, &nbsp;look into the lesson\r<BR>\n" );
document.write( "\n" );
document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/word/misc/Solving-minimax-problems-by--the-Linear-Programming-method.lesson>Solving minimax problems by the Linear Programming method</A> \r<BR>\n" );
document.write( "\n" );
document.write( "in this site.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "If you may want to look into my other solutions to minimax problems by the LP method in this forum, use the links \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "https://www.algebra.com/algebra/homework/coordinate/word/Linear_Equations_And_Systems_Word_Problems.faq.question.1131043.html\r<BR>\n" );
document.write( "\n" );
document.write( "https://www.algebra.com/algebra/homework/Finance/Finance.faq.question.1128383.html\r<BR>\n" );
document.write( "\n" );
document.write( "https://www.algebra.com/algebra/homework/Linear-equations/Linear-equations.faq.question.1123217.html\r<BR>\n" );
document.write( "\n" );
document.write( "https://www.algebra.com/algebra/homework/Finance/Finance.faq.question.1102103.html\r<BR>\n" );
document.write( "\n" );
document.write( "https://www.algebra.com/algebra/homework/word/finance/Money_Word_Problems.faq.question.1129285.html\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );