document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1142580>Question 1142580</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Maximize z = 2x1 + 3x2<BR>\n" );
document.write( "subject to: 2x1 + x2 ≤ 10<BR>\n" );
document.write( "9x1 + 3x2 ≤ 15<BR>\n" );
document.write( "x1 ≥ 0, x2 ≥ 0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #763257 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52909)</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=763257\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
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document.write( "1)  In the quadrant QI, draw the feasible domain.\r\n" );
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document.write( "    In this problem, it is a triangle adjacent to x- and y-axes and bounded by the line \r\n" );
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document.write( "        9x1 + 3x2 = 15.     (1)\r\n" );
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document.write( "    Find coordinates of its vertices.\r\n" );
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document.write( "    One vertex is (0,0), the origin of the coordinate system.\r\n" );
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document.write( "    Two other vertices are x- and y-intercepts of the line (2).\r\n" );
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document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28+330%2C+330%2C+-2.5%2C+12.5%2C+-2.5%2C+12.5%2C%0D%0A++++++++++10-2x%2C++%2815-9x%29%2F3%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r\n" );
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document.write( "    Lines  2x1 + x2 = 10 (read) and  9x1 + 3x2 = 15 (green)\r\n" );
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document.write( "2)  Calculate values of the objective function at these three vertices.\r\n" );
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document.write( "3)  Of the three values of the objective function at vertices of the triangle choose maximum value.\r\n" );
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document.write( "    This value is the maximum value of the objective function in the feasible domain.\r\n" );
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document.write( "    The vertex which provides this maximum value, will give you the solution point to the problem.\r\n" );
document.write( "</PRE>\r<BR>\n" );
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document.write( "That's it.\r<BR>\n" );
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document.write( "============\r<BR>\n" );
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document.write( "To see other similar problems solved by the Linear Programming method, &nbsp;look into the lesson\r<BR>\n" );
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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" );
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document.write( "in this site.\r<BR>\n" );
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document.write( "Also, &nbsp;look into the solutions of other similar problems in the archive to this forum under the links\r<BR>\n" );
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document.write( "https://www.algebra.com/algebra/homework/Inequalities/Inequalities.faq.question.1142000.html \r<BR>\n" );
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document.write( "https://www.algebra.com/algebra/homework/Sequences-and-series/Sequences-and-series.faq.question.1137172.html\r<BR>\n" );
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document.write( "https://www.algebra.com/algebra/homework/Graphs/Graphs.faq.question.1136382.html\r<BR>\n" );
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document.write( "https://www.algebra.com/algebra/homework/Coordinate-system/Coordinate-system.faq.question.1134444.html\r<BR>\n" );
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document.write( "https://www.algebra.com/algebra/homework/Graphs/Graphs.faq.question.1131906.html\r<BR>\n" );
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document.write( "https://www.algebra.com/algebra/homework/coordinate/word/Linear_Equations_And_Systems_Word_Problems.faq.question.1131043.html\r<BR>\n" );
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document.write( "https://www.algebra.com/algebra/homework/word/finance/Money_Word_Problems.faq.question.1129285.html\r<BR>\n" );
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document.write( "https://www.algebra.com/algebra/homework/Finance/Finance.faq.question.1128383.html  \r<BR>\n" );
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document.write( "https://www.algebra.com/algebra/homework/Linear-equations/Linear-equations.faq.question.1123217.html  \r<BR>\n" );
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document.write( "https://www.algebra.com/algebra/homework/playground/test.faq.question.1112482.html\r<BR>\n" );
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document.write( "https://www.algebra.com/algebra/homework/Finance/Finance.faq.question.1102103.html\r<BR>\n" );
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document.write( " </SPAN>\n" );
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