document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1065033>Question 1065033</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Consider the following linear program:<BR>\n" );
document.write( "Max 1A+2B<BR>\n" );
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document.write( "1A	&#8804;5<BR>\n" );
document.write( "1B&#8804;5<BR>\n" );
document.write( "2A+2B=12<BR>\n" );
document.write( "A,B&#8805;0<BR>\n" );
document.write( "	a.Show the feasible region<BR>\n" );
document.write( "	b.What are the extreme points of the feasible region?<BR>\n" );
document.write( "	c.Find the optimal solution using the graphical procedure.<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 #680162 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=680162\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> to use online graphing software, let x = A and let y = B.<BR>\n" );
document.write( "this changes your inequalities and equations as follows:\r<BR>\n" );
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document.write( "maximize x + 2y, such that:<BR>\n" );
document.write( "x <= 5<BR>\n" );
document.write( "y <= 5<BR>\n" );
document.write( "2x + 2y = 12<BR>\n" );
document.write( "x,y >= 0\r<BR>\n" );
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document.write( "you would graph the equations.\r<BR>\n" );
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document.write( "those would be:\r<BR>\n" );
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document.write( "x = 5<BR>\n" );
document.write( "y = 5<BR>\n" );
document.write( "2x + 2y = 12<BR>\n" );
document.write( "x = 0<BR>\n" );
document.write( "y = 0\r<BR>\n" );
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document.write( "you would then find the region of feasibility by looking at the areas on the graph that satisfy the inequalities and equations.\r<BR>\n" );
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document.write( "those would be:\r<BR>\n" );
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document.write( "x >= 5<BR>\n" );
document.write( "y >= 5<BR>\n" );
document.write( "2x + 2y = 12 (this is an equation and not an inqquality)<BR>\n" );
document.write( "x >= 0<BR>\n" );
document.write( "y >= 0\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/2017/012101.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( "you can see that your feasible region is the area on the graph that is:\r<BR>\n" );
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document.write( "on or below the line y = 5<BR>\n" );
document.write( "on or to the left of the line x = 5<BR>\n" );
document.write( "on or above the line y = 0<BR>\n" );
document.write( "on or to the right of the line x = 0<BR>\n" );
document.write( "on the line 2x + 2y = 12\r<BR>\n" );
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document.write( "what this says is that your solution has to:\r<BR>\n" );
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document.write( "be on the line of 2x + 2y = 12<BR>\n" );
document.write( "have an x-coordinate that is greater than or equal to 0 and less than or equal to 5.<BR>\n" );
document.write( "have a y-coordinate that is greater than or equal to 0 and less than or equal to 5.\r<BR>\n" );
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document.write( "your max/min balue should be at the corner points of the feasible region.\r<BR>\n" );
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document.write( "those corner points would be at (x,y) = (1,5) and (x,y) = (5,1)\r<BR>\n" );
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document.write( "i plotted some other points on the line just to show you that the max/min value is indeed on the corner points of the feasible region.\r<BR>\n" );
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document.write( "the values i got for x + 2y at the following coordinates are:\r<BR>\n" );
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document.write( "(1,5) = 11<BR>\n" );
document.write( "(2,4) = 10<BR>\n" );
document.write( "(3,3) = 9<BR>\n" );
document.write( "(4,2) = 8<BR>\n" );
document.write( "(5.1) = 7\r<BR>\n" );
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document.write( "your maximum solution is at the coordinate of (1,5).\r<BR>\n" );
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document.write( "all of your constraints have to be satisfied.\r<BR>\n" );
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document.write( "at the point (1,5):\r<BR>\n" );
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document.write( "x <= 5 is satisfied because x = 1<BR>\n" );
document.write( "y <= 5 is satisfied because y = 5<BR>\n" );
document.write( "x >= 0 is satisfied because x = 1<BR>\n" );
document.write( "y >= 0 is satisfied because y = 5<BR>\n" );
document.write( "2x + 2y = 12 is satisfied because 2*1 + 2*5 = 2 + 10 = 12\r<BR>\n" );
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document.write( "your solution is that the maximum value is when x = 1 and y = 5.\r<BR>\n" );
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document.write( "that is one of the corner points of the feasible region.\r<BR>\n" );
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