document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1206461>Question 1206461</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Minimize Z=2X+Y<BR>\n" );
document.write( "3Y+4X≥24<BR>\n" );
document.write( "3Y+2X≥16<BR>\n" );
document.write( "Subject to2Y+2X≥14<BR>\n" );
document.write( "X≥0<BR>\n" );
document.write( "Y≥0	\r<BR>\n" );
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document.write( "X=<BR>\n" );
document.write( "Y=	 <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 #843977 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=843977\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> i think you mean:\r<BR>\n" );
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document.write( "minimize z = 2x + y subject to<BR>\n" );
document.write( "3y + 4x >= 24<BR>\n" );
document.write( "3y + 2x >= 16<BR>\n" );
document.write( "2y + 2x >= 14<BR>\n" );
document.write( "x >= 0<BR>\n" );
document.write( "y >= 0\r<BR>\n" );
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document.write( "using the desmos.com calculator, you would graph the opposite of the inequalities.<BR>\n" );
document.write( "the area of the graph not shaded is the region of feasibility.<BR>\n" );
document.write( "the corner points of the region of feasibility will contain the minimum value of the objective function.\r<BR>\n" );
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document.write( "the objective function is z = 2x + y.\r<BR>\n" );
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document.write( "the corner points of the feasible region are:\r<BR>\n" );
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document.write( "(0,8)<BR>\n" );
document.write( "(3,4)<BR>\n" );
document.write( "(5,2)<BR>\n" );
document.write( "(8,0)\r<BR>\n" );
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document.write( "the minimum value of z = 2x + y is at the point (0,8), where z = 8.\r<BR>\n" );
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document.write( "all the constraints are satisfied.\r<BR>\n" );
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document.write( "you get:\r<BR>\n" );
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document.write( "3y + 4x >= 24 becomes 3*8 + 4*0 = 24 >= 24 which is true.<BR>\n" );
document.write( "3y + 2x >= 16 becomes 3*8 + 2*0 = 24 >= 16 which is true.<BR>\n" );
document.write( "2y + 2x >= 14 becomes 2*8 + 2*0 = 16 >= 14 which is true.<BR>\n" );
document.write( "x >= 0 becomes 0 >= 0 which is true.<BR>\n" );
document.write( "y >= 0 becomes 8 >= 0 which is true.\r<BR>\n" );
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document.write( "the value of z is minimum when x = 0 and y = 8.\r<BR>\n" );
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document.write( "here's what the graph looks like.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2024/031301.jpg\">\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );