document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1082166>Question 1082166</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find two real numbers x and y such that 2x+y=80 and A=xy is maximum </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #696247 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52786)</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=696247\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "Find two real numbers x and y such that 2x+y=80 and A=xy is maximum<BR>\n" );
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document.write( "From 2x + y = 80 you have y = 80-2x.\r\n" );
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document.write( "Then A = xy = x*(80-2x), and you need to find the maximum of this quadratic function.\r\n" );
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document.write( "The zeros are at x = 0 and x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=80%2F2 ALIGN=MIDDLE  ALT=\"80%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 40.\r\n" );
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document.write( "Hence, the maximum is achieved at x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=40%2F2 ALIGN=MIDDLE  ALT=\"40%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 20, exactly at the mid-point between the zeroes.\r\n" );
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document.write( "Then the maximum value of A is A = x*(80-2x) = 20*(80-2*20) = 20*40 = 800.\r\n" );
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document.write( "Solved.\r<BR>\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+-5.5%2C+50.5%2C+-100.5%2C+1000.5%2C%0D%0A++++++++++x%2A%2880-2x%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Plot y = x*(80-2x)\r<BR>\n" );
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document.write( "My other lessons in this site on finding the maximum/minimum of a quadratic function are \r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/HOW-TO-complete-the-square-of-a-quadratic-function-to-find-its-minimum-maximum.lesson>HOW TO complete the square to find the minimum/maximum of a quadratic function</A>\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/Briefly-on-How-to-complete-the-square-of-a-quadratic-function-to-find-its-minimum-maximum.lesson>Briefly on finding the minimum/maximum of a quadratic function</A>\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/HOW-TO-complete-the-square-to-find-the-vertex-of-a-quadratic-function.lesson>HOW TO complete the square to find the vertex of a parabola</A>\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/Briefly-on-finding-the-vertex-of-a-parabola.lesson>Briefly on finding the vertex of a parabola</A>\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/A-rectangle-with-the-given-perimeter-which-has-the-maximal-area-is-a-square.lesson>A rectangle with a given perimeter which has the maximal area is a square</A>\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/A-farmer-planning-to-fence-a-rectangular-garden-to-enclose-the-maximal-area.lesson>A farmer planning to fence a rectangular garden to enclose the maximal area</A>\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/A-farmer-planning-to-fence-a-rectangular-area-along-the-river--to-enclose-the-maximal-area.lesson>A farmer planning to fence a rectangular area along the river to enclose the maximal area</A>\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/A-rancher-planning-to-fence-two-adjacent-rectangular-corrals-to-enclose-the-maximal-area-.lesson>A rancher planning to fence two adjacent rectangular corrals to enclose the maximal area</A>\r<BR>\n" );
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document.write( "Also, you have this free of charge online textbook in ALGEBRA-I in this site\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-I - YOUR ONLINE TEXTBOOK</A>.\r<BR>\n" );
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document.write( "The referred lessons are the part of this textbook under the topic \"<U>Finding minimum/maximum of quadratic functions</U>\". \r<BR>\n" );
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