document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1140867>Question 1140867</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A farmer has a field of 70 acres in which he plants potatoes and corn. The seed for potatoes costs $20/acre, the seed for corn costs $60/acre, and the farmer has set aside $3000 to spend on seed. The profit per acre of potatoes is $150 and the profit for corn is $50 an acre. How many acres of each should the farmer plant? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #761391 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=761391\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> total acres are 70.<BR>\n" );
document.write( "farmer has seeds to plan either potatoes or corn or both.<BR>\n" );
document.write( "seed for potatoes is 20 dollars per acre.<BR>\n" );
document.write( "see for corn is 60 dollars per acre.<BR>\n" );
document.write( "total money for seed is 3000.<BR>\n" );
document.write( "profit per acre of potatoes is 150 dollars.<BR>\n" );
document.write( "profit per acre of corn is 50 dollars.\r<BR>\n" );
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document.write( "this problem can be solved graphically.\r<BR>\n" );
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document.write( "x = number of acres of potatoes<BR>\n" );
document.write( "y = number of acres of corn.\r<BR>\n" );
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document.write( "objective function is profit = 150 * x + 50 * y\r<BR>\n" );
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document.write( "this is the function you want to maximize.\r<BR>\n" );
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document.write( "constraints are:\r<BR>\n" );
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document.write( "x >= 0<BR>\n" );
document.write( "y >= 0<BR>\n" );
document.write( "20 * x + 60 * y <= 3000<BR>\n" );
document.write( "x + y <= 70\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 your region of feasibility.\r<BR>\n" );
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document.write( "the corner points of this area will be where the maximum profit lies.\r<BR>\n" );
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document.write( "the graph looks like this:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2019/051103.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "the corner points of the reasible region are:\r<BR>\n" );
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document.write( "(0,50), (30,40), (70,0), (0,0)\r<BR>\n" );
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document.write( "profit at each of these corner points are:\r<BR>\n" );
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document.write( "0 * 150 + 50 * 50 = 2500 for (0,50)<BR>\n" );
document.write( "30 * 150 + 40 * 50 = 6500 for (30,40)<BR>\n" );
document.write( "70 * 150 + 0 * 50 = 10500 for (70,0) *****<BR>\n" );
document.write( "0 * 150 + 0 * 50 = 0 for (0,0)\r<BR>\n" );
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document.write( "maximum profit is attained when all 70 acres are planted by potatoes.\r<BR>\n" );
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document.write( "all constraints need to be satisfied as well.\r<BR>\n" );
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document.write( "constraints are:\r<BR>\n" );
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document.write( "x >= 0 = satisfied<BR>\n" );
document.write( "y >= 0 = satisfied<BR>\n" );
document.write( "20 * x + 60 * y <= 3000 = 20 * 70 + 60 * 0 <=3000 = 1400 <= 3000 = satisfied<BR>\n" );
document.write( "x + y <= 70 = 70 + 0 <= 70 = 70 <= 70 = satisfied.\r<BR>\n" );
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document.write( "all constraints were satisfied, therefore the solution looks good.\r<BR>\n" );
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document.write( "the solution is that all 70 acres should be planted by potatoes for maximum profit, based on the information provided in the problem.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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