document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1141999>Question 1141999</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve the linear programming problem by the method of corners. <BR>\n" );
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" );
document.write( "at <BR>\n" );
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document.write( "The maximum is P = <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 #762691 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=762691\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> using the desmos.com calculator, you would graph the opposite of the constraint inequalities\r<BR>\n" );
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document.write( "the constraints are:\r<BR>\n" );
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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<BR>\n" );
document.write( "y ≥ 0\r<BR>\n" );
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document.write( "you would graph:\r<BR>\n" );
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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<BR>\n" );
document.write( "y <= 0 \r<BR>\n" );
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document.write( "the graph looks like this.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2019/060904.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "the area of the graph that is not shaded is your region of feasibility.\r<BR>\n" );
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document.write( "the corner points of that region are where the maximum / minimum value of the objective function lies.\r<BR>\n" );
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document.write( "the objective function is p 5x + 4y\r<BR>\n" );
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document.write( "the corner points on the graph are:\r<BR>\n" );
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document.write( "(2.8, 7.6)<BR>\n" );
document.write( "(.769, 3.538)<BR>\n" );
document.write( "(5, 1)\r<BR>\n" );
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document.write( "these results are in (x,y) format.\r<BR>\n" );
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document.write( "evaluation of 5x + 4y for each yields.\r<BR>\n" );
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document.write( "(2.8, 7.6) results in 44.4<BR>\n" );
document.write( "(.769, 3.538) results in 17.997<BR>\n" );
document.write( "(5, 1) results in 29\r<BR>\n" );
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document.write( "the maximum value is 44.4 at (2.8, 7.6)\r<BR>\n" );
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document.write( "the minimum value is 17.997 at (.769, 3.538)\r<BR>\n" );
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document.write( " </SPAN>\n" );
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