document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1136382>Question 1136382</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 $20 per acre. Seed for crop B costs $40 per acre. The farmer can spend at most $2200 on seed.\r<BR>\n" );
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document.write( "If crop B brings in a profit of $190 per acre, and crop A brings in a profit of $110 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 #754149 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=754149\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
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document.write( "Let X = acres for A  and  Y = acres for B.\r\n" );
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document.write( "The farmer wants to maximize his profit  \r\n" );
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document.write( "    P(X,Y) = 110*X + 190*Y\r\n" );
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document.write( "under these restrictions\r\n" );
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document.write( "    X + Y = 60,\r\n" );
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document.write( "    20*X + 40*Y <= 2200,\r\n" );
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document.write( "    X >= 0,  Y >= 0.\r\n" );
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document.write( "The feasible domain is shown in the Figure below.\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%2C+100%2C+-10%2C+100%2C%0D%0A++++++++++60-x%2C+%282200-20x%29%2F40%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r\n" );
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document.write( "Plot X + Y = 60 (red)  and  20X + 40Y = 2200 (green)\r\n" );
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document.write( "The feasibility domain is the quadrilateral in QI below the red and green lines.\r\n" );
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document.write( "Corner points of the quadrilateral (its vertices) are\r\n" );
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document.write( "    P1 = (0,0)\r\n" );
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document.write( "    P2 = (0,55)   (y-intercept of the green line)\r\n" );
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document.write( "    P3 = (10,50)  (intersection point of red and green line).\r\n" );
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document.write( "    P4 = (60,0)    (x-intercept of the red line)\r\n" );
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document.write( "The values of the profit function in the corner points are:\r\n" );
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document.write( "    P1:  P( 0, 0) = 0\r\n" );
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document.write( "    P2:  P( 0,55) = 110*0  + 190*55 = 10450\r\n" );
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document.write( "    P3:  P(10,50) = 110*10 + 190*50 = 10600\r\n" );
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document.write( "    P4:  P(60,0)  = 110*60 + 190*0  = 6600.\r\n" );
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document.write( "The maximal value of the profit function is achieved at the points P3.\r\n" );
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document.write( "It means that the optimal solution is 10 acres for A and 50 acres for B.\r\n" );
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document.write( "It gives the profit of 16000 dollars.\r\n" );
document.write( "</PRE>\r<BR>\n" );
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document.write( "Solved.\r<BR>\n" );
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document.write( "--------------------\r<BR>\n" );
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document.write( "To see other similar problems solved by the Linear Programming method, &nbsp;look into the lesson\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/word/misc/Solving-minimax-problems-by--the-Linear-Programming-method.lesson>Solving minimax problems by the Linear Programming method</A> \r<BR>\n" );
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document.write( "in this site.\r<BR>\n" );
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document.write( "Also, &nbsp;look into the solutions of other similar problems in the archive to this forum under the links\r<BR>\n" );
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document.write( "https://www.algebra.com/algebra/homework/Coordinate-system/Coordinate-system.faq.question.1134444.html\r<BR>\n" );
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document.write( "https://www.algebra.com/algebra/homework/Graphs/Graphs.faq.question.1131906.html\r<BR>\n" );
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document.write( "https://www.algebra.com/algebra/homework/coordinate/word/Linear_Equations_And_Systems_Word_Problems.faq.question.1131043.html\r<BR>\n" );
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document.write( "https://www.algebra.com/algebra/homework/word/finance/Money_Word_Problems.faq.question.1129285.html\r<BR>\n" );
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document.write( "https://www.algebra.com/algebra/homework/Finance/Finance.faq.question.1128383.html\r<BR>\n" );
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document.write( "https://www.algebra.com/algebra/homework/Linear-equations/Linear-equations.faq.question.1123217.html\r<BR>\n" );
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document.write( "https://www.algebra.com/algebra/homework/playground/test.faq.question.1112482.html\r<BR>\n" );
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document.write( "https://www.algebra.com/algebra/homework/Finance/Finance.faq.question.1102103.html\r<BR>\n" );
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document.write( " </SPAN>\n" );
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