document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1162265>Question 1162265</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A farm co-op wants to grow corn and soybeans.  Each acre of corn requires 7 gallons of fertilizer and 0.50 hours to harvest.  Each acre of soybeans requires 3 gallons of fertilizer and 1 hour to harvest.  The co-op has available at most 40,500 gallons of fertilizer and 5,250 hours of labor for harvesting.  If the profits per acre are $50 for corn and $45 for soybeans, how many acres of each should the co-op plant to maximize their profit?  What is the maximum profit?\r<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 #786053 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=786053\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> x = number of acres of corn.<BR>\n" );
document.write( "y = number of acres of soybeans.\r<BR>\n" );
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document.write( "make a table as shown below:\r<BR>\n" );
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document.write( "                             x                   y\r\n" );
document.write( "                           corn              soybeans\r\n" );
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document.write( "fertilizer gallons           7                   3         <= 40,500\r\n" );
document.write( "harvest hours                .5                  1         <= 5,250\r\n" );
document.write( "profit                       50                  45        maximize\r\n" );
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document.write( "using the desmos.com calculator, graph the opposite of the constraints and then evaluate the objective function at the corner points of the feasible region.\r<BR>\n" );
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document.write( "the constraint functions are:\r<BR>\n" );
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document.write( "7x + 3y <= 40,500<BR>\n" );
document.write( ".5x + y <= 5250<BR>\n" );
document.write( "x,y >= 0\r<BR>\n" );
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document.write( "the objective function is:\r<BR>\n" );
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document.write( "profit = 50x + 45y\r<BR>\n" );
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document.write( "you are graphing the OPPOSITE of the constraint inequalities.\r<BR>\n" );
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document.write( "here's what the graph looks like:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2020/071301.jpg\" >\r<BR>\n" );
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document.write( "maximum profit is at the point (4500,3000).<BR>\n" );
document.write( "profit is 50*4500 + 45*3000 = 360,000<BR>\n" );
document.write( "gallons of fertilizer used are 4500*7 + 3000*3 = 40,500 <= 40,500<BR>\n" );
document.write( "hours of labor = 4500*.5 + 3000*1 = 5250 <= 5250\r<BR>\n" );
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document.write( "looks like all the available resources were used when the maximum profit was attained.\r<BR>\n" );
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