document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1058105>Question 1058105</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Linear Programming - The Graphical Method\r<BR>\n" );
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document.write( "A farmer is going to divide her 60 acre farm between two crops. Seed for crop A costs $20 per acre. Seed for crop B costs $10 per acre. The farmer can spend at most $700 on seed. If crop B brings in a profit of $60 per acre, and crop A brings in a profit of $180 per acre, how many acres of each crop should the farmer plant to maximize her profit? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #673166 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52781)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=673166\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "Linear Programming - The Graphical Method\r<BR>\n" );
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document.write( "A farmer is going to divide her 60 acre farm between two crops. <BR>\n" );
document.write( "Seed for crop A costs $20 per acre. Seed for crop B costs $10 per acre. <BR>\n" );
document.write( "The farmer can spend at most $700 on seed. If crop B brings in a profit of $60 per acre, and crop A brings in a profit of $180 per acre, <BR>\n" );
document.write( "how many acres of each crop should the farmer plant to maximize her profit?<BR>\n" );
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document.write( "Your restriction equations are\r\n" );
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document.write( "x + y = 60  acres   (1)   (for areas; x = the area for crop A;   y = the area for crop B).\r\n" );
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document.write( "20x + 10y = 700     (2)    for the seed cost.\r\n" );
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document.write( "Rewrite:\r\n" );
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document.write( " x + y = 60,        (1')\r\n" );
document.write( "2x + y = 70.        (2')\r\n" );
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document.write( "The additional obvious restrictions are x >= 0  and  y >= 0.\r\n" );
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document.write( "The plot is \r\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28+330%2C+330%2C+-10.5%2C+100.5%2C+-10.5%2C+100.5%2C%0D%0A++++++++++60-x%2C++70-2x%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r\n" );
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document.write( "Plots y = 60-x and y = 70-2x\r\n" );
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document.write( "Your area is a quadrilateral in QI restricted by the axes x- an y- and by the red and the green straight lines.\r<BR>\n" );
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document.write( "Your objective function is the profit z = 180x + 60y.\r<BR>\n" );
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document.write( "According to the conception/ideology of the linear programming method, you need to evaluate your <BR>\n" );
document.write( "objective function 180x + 60y in three points:\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp; y-intercept (x,y) = ( 0, 60);<BR>\n" );
document.write( "&nbsp;&nbsp;&nbsp;&nbsp; x-intercept (x,y) = (35, 0);<BR>\n" );
document.write( "&nbsp;&nbsp;&nbsp;&nbsp; and the point (x,y), which is the solution of the system (1'), (2') (the intersection point of the red and the green straight lines).\r<BR>\n" );
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document.write( "Then choose that point of the three, where the objective function is maximal.\r<BR>\n" );
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document.write( "Having this plan/instruction, you can complete the assignment on your own.\r<BR>\n" );
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document.write( "Good luck!\r<BR>\n" );
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document.write( " </SPAN>\n" );
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