document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1141944>Question 1141944</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve the linear programming problem by the method of corners.\r<BR>\n" );
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document.write( "Find the minimum and maximum of P = 5x + 4y subject to<BR>\n" );
document.write( "3x	 + 	5y	 ≥ 	20<BR>\n" );
document.write( "3x	 + 	y	 ≤ 	16<BR>\n" );
document.write( "−2x	 + 	y	 ≤ 	2<BR>\n" );
document.write( "x ≥ 0, y ≥ 0. <BR>\n" );
document.write( "The minimum is P =  <BR>\n" );
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document.write( "The maximum is P =  <BR>\n" );
document.write( " at <BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #762600 by </B><A HREF=/tutors/aboutme.mpl?userid=math_helper><B>math_helper(2461)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_helper><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=math_helper><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=762600\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> When you graph the three inequalities,  <BR>\n" );
document.write( "3x + 5y ≥ 20<BR>\n" );
document.write( "3x + y ≤ 16<BR>\n" );
document.write( "−2x + y ≤ 2\r<BR>\n" );
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document.write( "You will get a feasibility region in the shape of a triangle (the triangle is located in Q1 so x>=0 and y>=0 hold).  The corners of the triangle are at:<BR>\n" );
document.write( " (2.8,7.6)<BR>\n" );
document.write( " (5,1)<BR>\n" );
document.write( " (0.769,3.538)\r<BR>\n" );
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document.write( "Evaluating these (x,y) values in P = 5x + 4y gives:<BR>\n" );
document.write( " (2.8,7.6)       5x + 4y =  44.4      <<< max @ (2.8,7.6)<BR>\n" );
document.write( " (5,1)           5x + 4y =  29<BR>\n" );
document.write( " (0.769,3.538)   5x + 4y =  17.997    <<< min @ (0.769,3.538)\r<BR>\n" );
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document.write( "EDIT:  Added the Desmos graph (picture) below...\r<BR>\n" );
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