document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1175938>Question 1175938</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Using the rules of graphing systems of linear equations and inequalities; would you please construct a graph that best shows the area of each crop that can be planted? \r<BR>\n" );
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document.write( "A farm has an area of 50 Hectares (Ha). It is to be planted with tomatoes and potatoes. At most $8000 can be spent on planting. The planting cost for potatoes is $100/Ha and for tomatoes $200/Ha. Choose the graph that best shows the area of each crop that can be planted. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #801725 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=801725\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the two inequalities that need to be satisfied simultaneously are:\r<BR>\n" );
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document.write( "x + y <= 50<BR>\n" );
document.write( "100x + 200y <= 8000\r<BR>\n" );
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document.write( "using the desmos.com calculator, you would graph the opposite of these inequalities.\r<BR>\n" );
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document.write( "the area on the graph that is not shaded is the feasible region.\r<BR>\n" );
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document.write( "the feasible region includes any point on the graph that lies on the line x = 0, y = 0, x + y = 50, and 100x + 200y = 8000, as well as in the unshaded ara of the graph,  because the inequalities are inclusive of the points on those lines, i.e. they are <= rather than <, and >= rather than >.\r<BR>\n" );
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document.write( "your graph will look something like this.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2021/022604.jpg\" >\r<BR>\n" );
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document.write( "the points in red are outside the feasible region.<BR>\n" );
document.write( "they do not satisfy all the constraints.\r<BR>\n" );
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document.write( "the points in black are inside the feasible region.<BR>\n" );
document.write( "they do satisfy all the constraints.\r<BR>\n" );
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document.write( "for example:\r<BR>\n" );
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document.write( "the point (20,30) is in the feasible region.<BR>\n" );
document.write( "it satisfies the constraint functions.\r<BR>\n" );
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document.write( "the point (40,30) is not in the feasible region.<BR>\n" );
document.write( "it does not satisfy the constraint functions.\r<BR>\n" );
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document.write( "the constraint functions are:\r<BR>\n" );
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document.write( "x + y <= 50<BR>\n" );
document.write( "100x + 200y <= 8000\r<BR>\n" );
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document.write( "at the point (20,30), x + y = 30 which is <=  30 and 100x + 200y = 8000 which is <= 8000.<BR>\n" );
document.write( "that point is in the f3easible region and satisfies all the constraints.\r<BR>\n" );
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document.write( "at the point (40,30), x + y = 70 which is not <= 50 and 100x + 200y = 10,000 which is not <= 8000.<BR>\n" );
document.write( "that point is not in the feasible region and does not satisfy all the constraints.\r<BR>\n" );
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document.write( "note that all the constraints need to be satisfied.  failure to satisfy any one of the constraint is enough to make the point not feasible.\r<BR>\n" );
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document.write( "for example, the point (50,10) gives you the following results.\r<BR>\n" );
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document.write( "x + y = 60 which is not <= 50 and so it does not satisfy the x + y <= 50 constraint.\r<BR>\n" );
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document.write( "100x + 200y = 7000 which is <= 8000 and so it does satisfy the 100x + 200y <= 8000 constraint.\r<BR>\n" );
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document.write( "since the point (30,10) doesn't satisfy all of the constrains it is not in the feasible region.\r<BR>\n" );
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document.write( "this can be seen on the graph because it is in the shaded region.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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