document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=959083>Question 959083</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve the linear programming problem by the method of corners.<BR>\n" );
document.write( "Minimize	C = 4x + 3y     <BR>\n" );
document.write( "subject to  	x	 + 	y	 &#8804; 	48<BR>\n" );
document.write( "x	 + 	3y	 &#8805; 	60<BR>\n" );
document.write( "9x	 + 	5y	 &#8804; 	320<BR>\n" );
document.write( "x &#8805; 10, y &#8805; 0   \r<BR>\n" );
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document.write( "What is the minimum C? What is the point (X,Y)? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #586287 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=586287\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Solve the linear programming problem by the method of corners.<BR>\n" );
document.write( "Minimize C = 4x + 3y<BR>\n" );
document.write( "subject to x + y &#8804; 48<BR>\n" );
document.write( "x + 3y &#8805; 60<BR>\n" );
document.write( "9x + 5y &#8804; 320<BR>\n" );
document.write( "x &#8805; 10, y &#8805; 0<BR>\n" );
document.write( "What is the minimum C? What is the point (X,Y)?\r<BR>\n" );
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document.write( "solve for y in the constraint equations.\r<BR>\n" );
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document.write( "you get:\r<BR>\n" );
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document.write( "x + y <= 48 becomes y <= (48 - x)\r<BR>\n" );
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document.write( "x + 3y >= 60 becomes y >= (60 - x)/3\r<BR>\n" );
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document.write( "9x + 5y <= 320 becomes y <= (320 - 9x) / 5\r<BR>\n" );
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document.write( "you also have the additional constraints of x >= 10 and y >= 0.\r<BR>\n" );
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document.write( "you will graph the equality portion of these constraints and then you will fill in the area that satisfies all the inequality portions of the constraints.\r<BR>\n" );
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document.write( "your graph will look like this:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2015/032803.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( "the corner points of your feasible region are:\r<BR>\n" );
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document.write( "(10,38)<BR>\n" );
document.write( "(20,28)<BR>\n" );
document.write( "(10,16 and 2/3)<BR>\n" );
document.write( "(30,10)\r<BR>\n" );
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document.write( "you evaluate your objective function of 4x + 3y at each of these corner points.\r<BR>\n" );
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document.write( "you will find that the minimum solution is at the point (10, 16 and 2/3) where the value of 4x + 3y is equal to 90.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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