document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1184214>Question 1184214</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A farmer is going to divide her 60 acre farm between two crops. Seed for crop A costs $30 per acre. Seed for crop B costs $15 per acre. The farmer can spend at most $1200 on seed.\r<BR>\n" );
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document.write( "If crop B brings in a profit of $80 per acre, and crop A brings in a profit of $120 per acre, how many acres of each crop should the farmer plant to maximize her profit?\r<BR>\n" );
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document.write( "   acres of crop A<BR>\n" );
document.write( "   acres of crop B </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #815167 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=815167\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> x = number of acres for crop A.<BR>\n" );
document.write( "y = number of acres for crop B.\r<BR>\n" );
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document.write( "your objective function is equal to 120x + 80y.<BR>\n" );
document.write( "this is the profit function that you want to maximize the value of.\r<BR>\n" );
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document.write( "your constraint functions are:<BR>\n" );
document.write( "x + y <= 60 (acres)<BR>\n" );
document.write( "30x + 15y <= 1200 (money spent on seeds)<BR>\n" );
document.write( "x >= 0, y >= 0 (must not be negative)\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( "specifically, you would graph:<BR>\n" );
document.write( "x + y >= 60<BR>\n" );
document.write( "30x + 15y >= 1200<BR>\n" );
document.write( "x <= 0, y <= 0\r<BR>\n" );
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document.write( "the area on the graph that is not shaded is your region of feasibility.\r<BR>\n" );
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document.write( "the corner points of this region are where the maximum profit lies.\r<BR>\n" );
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document.write( "all the constraints must be met at the corner point where the maximum profit lies.\r<BR>\n" );
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document.write( "the graph is shown below:\r<BR>\n" );
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document.write( "the maximum profit is at the point (x,y) = (20,40).\r<BR>\n" );
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document.write( "at this point, the profit is 120x + 80y = 5600.<BR>\n" );
document.write( "the number of acres is x + y = 60.<BR>\n" );
document.write( "the amount spent on seeds is 30x + 15y = 1200.<BR>\n" );
document.write( "all values of x and y are greater than or equal to 0.\r<BR>\n" );
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document.write( "your solution is that the farmer should plant 20 acres of crop A and 40 acres of crop B to maximize profits.\r<BR>\n" );
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document.write( "here's a picture of what the graph shows.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2021/091301.jpg\" >\r<BR>\n" );
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document.write( "the graphing calculator can be found at <a  rel=nofollow HREF= \"https://www.desmos.com/calculator\" target = \"_blank\">https://www.desmos.com/calculator</a>\r<BR>\n" );
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document.write( " </SPAN>\n" );
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