document.write( "Question 1118359: Please help me to understand how to do \"optimization\"\r
\n" ); document.write( "\n" ); document.write( "Objective function: C = 8x+10y Maximize
\n" ); document.write( "Constraints
\n" ); document.write( "2x+y _< 12
\n" ); document.write( "x+3y _< 21\r
\n" ); document.write( "\n" ); document.write( "X_>0, y_>0\r
\n" ); document.write( "\n" ); document.write( "Then I need to graph it?
\n" ); document.write( " \n" ); document.write( "
Algebra.Com's Answer #733657 by ikleyn(52790)\"\" \"About 
You can put this solution on YOUR website!
\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "1.  The notice that @greenestamps made in his post, is very well known fact,\r\n" );
document.write( "\r\n" );
document.write( "    and it is very well known to those who is familiar with more advanced courses in Linear Programming.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "2.  Since you, the student, are in the very beginning stage of learning this method, you may follow the method\r\n" );
document.write( "\r\n" );
document.write( "    presented by @ankor@dixie-net.com\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    I also recommend you to read my introductory lesson\r\n" );
document.write( "          Solving minimax problems by the Linear Programming method \r\n" );
document.write( "    in this site, which is a standard exposition of the method in all details for the beginner student. \r\n" );
document.write( "\r\n" );
document.write( "    It is the best exposition to start with . . . \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "3.  For @greenestapms info, the college textbook, containing the conception he refers to, is (for example) this one:\r\n" );
document.write( "\r\n" );
document.write( "    \"College Mathematics for management, life and social science\"\r\n" );
document.write( "     3rd edition, R.A.Barnett and M.R.Ziegler, 1984, San Francisco, ISBN 0-02-306220-7.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "4.  Linear Programming method is very advanced and very well developed industrial optimization method now.\r\n" );
document.write( "\r\n" );
document.write( "    It works in 2D (in plane, and students learn it in introductory geometric version, as it is presented in this post),\r\n" );
document.write( "\r\n" );
document.write( "    in 3D, where visual interpretation is not so easy, and then as a quite abstract method in multi-dimensional spaces \r\n" );
document.write( "\r\n" );
document.write( "       (with 100, 1000 or even 10000 and more dimensions . . . ), where geometric intuition does not work at all.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    For each of these stages, the interested reader may find textbooks of relevant levels.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "5.  For those who knows the method in all details, it might be the way to earn money for life.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "6.  For the history of the method and many interesting details/applications, see this Wikipedia article\r\n" );
document.write( "\r\n" );
document.write( "    https://en.wikipedia.org/wiki/Linear_programming\r\n" );
document.write( "
\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
\n" );