document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=999941>Question 999941</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Why are these two similar problems set up differently? and why are they set up in that way at all?\r<BR>\n" );
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document.write( "Find two numbers whose difference is 60 and whose product is a minimum? Why does this use f(x) = x(x-60)\r<BR>\n" );
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document.write( "and\r<BR>\n" );
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document.write( "Find two numbers whose sum is 60 and whose product is a maximum? Why does this one use f(x) = x(60-x)\r<BR>\n" );
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document.write( "I fundamentally don't understand what is happening and how that function was created at all.<BR>\n" );
document.write( "And will there ever be a case where it's a difference and the product is a maximum. Or where it's a sum and the product is a minimum. I don't understand what this question is asking.\r<BR>\n" );
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document.write( "So confused...<BR>\n" );
document.write( "Please help! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #617482 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=617482\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let the two numbers be x and y.<BR>\n" );
document.write( "Assume x is larger than y.<BR>\n" );
document.write( "The sum would be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By=60 ALIGN=MIDDLE  ALT=\"x%2By=60\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=60-x ALIGN=MIDDLE  ALT=\"y=60-x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So the product of the two numbers is,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%5B1%5D=x%2Ay=x%2860-x%29 ALIGN=MIDDLE  ALT=\"P%5B1%5D=x%2Ay=x%2860-x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The difference of 60 would be,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-y=60 ALIGN=MIDDLE  ALT=\"x-y=60\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x-60 ALIGN=MIDDLE  ALT=\"y=x-60\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So the product of the two numbers is,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%5B2%5D=x%2Ay=x%28x-60%29 ALIGN=MIDDLE  ALT=\"P%5B2%5D=x%2Ay=x%28x-60%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Yes, you can set up a problem however you want. <BR>\n" );
document.write( "Sometimes it won't make sense. <BR>\n" );
document.write( "Example: Make a shape using 40' of wire so that the enclosed shape has the minimum area. You could just make a straight line of 4 lengths of 10' of wire so that the enclosed area is zero. <BR>\n" );
document.write( "Well if you're a farmer and you want to make a pen, <BR>\n" );
document.write( "why would you want the minimum area, <BR>\n" );
document.write( "you'd want the maximum area for your animals to graze. </SPAN>\n" );
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