document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1026931>Question 1026931</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Given that xy = 3/2 and both x and y are nonnegative real numbers, find the minimum value of 10x + (3y)/(5). </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #642213 by </B><A HREF=/tutors/aboutme.mpl?userid=robertb><B>robertb(5830)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=robertb><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=robertb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=642213\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> First of all, x and y cannot be zero because of the condition xy = 3/2.  Hence x and y can only be positive.\r<BR>\n" );
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document.write( "Now let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=F%28x%2Cy%29+=+10x+%2B+%283y%29%2F5 ALIGN=MIDDLE  ALT=\"F%28x%2Cy%29+=+10x+%2B+%283y%29%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+3%2F%282x%29 ALIGN=MIDDLE  ALT=\"y+=+3%2F%282x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, ==> F(x,y) becomes, after substitution, \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=F%28x%29+=+10x+%2B+9%2F%2810x%29 ALIGN=MIDDLE  ALT=\"F%28x%29+=+10x+%2B+9%2F%2810x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "==> F'(x) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10+-+9%2F%2810x%5E2%29 ALIGN=MIDDLE  ALT=\"10+-+9%2F%2810x%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Setting this to 0 to find the critical point, we get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10+=+9%2F%2810x%5E2%29 ALIGN=MIDDLE  ALT=\"10+=+9%2F%2810x%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+=+9%2F100 ALIGN=MIDDLE  ALT=\"x%5E2+=+9%2F100\"   DISABLED_style= \"max-width:90%; height:auto;\" > ==> x = 3/10.  (Chose the positive because of the hypothesis.)<BR>\n" );
document.write( "==> y = 5.<BR>\n" );
document.write( "Now the 2nd derivative is F\" = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%2F%285x%5E3%29+%3E+0 ALIGN=MIDDLE  ALT=\"9%2F%285x%5E3%29+%3E+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > when x = 3/10.<BR>\n" );
document.write( "Hence an (absolute) minimum exists at (3/10,5), with value<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=F%283%2F10%2C5%29+=+10%283%2F10%29+%2B+%283%2A5%29%2F5+=+6 ALIGN=MIDDLE  ALT=\"F%283%2F10%2C5%29+=+10%283%2F10%29+%2B+%283%2A5%29%2F5+=+6\"   DISABLED_style= \"max-width:90%; height:auto;\" >. </SPAN>\n" );
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