document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1190566>Question 1190566</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1) Profit per tree grown and sold depends upon the height of tree at the time of sale. Taking h as tree height in metres, profit of tree in thousands Tanzanian shillings is approximated as: P(h) = (10 + 2h) ^ (1/2) - 0.1h (1) What tree height provides maximum profit per tree? (2) What is the maximum profit per tree? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #822269 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=822269\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> your equation is p(h) = (10 + 2h) ^ (1/2) - .1h.<BR>\n" );
document.write( "the equation for graphing is y = (10 + 2x) ^ (1/2) - .1x.<BR>\n" );
document.write( "for graphing, y takes the place of p(h) and x takes the place of h.\r<BR>\n" );
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document.write( "here is a graph of the equation.\r<BR>\n" );
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document.write( "the graph shows the maximum profit is 5.5, when h = 45.\r<BR>\n" );
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document.write( "i'm not sure how else you would find it unless you used calculus and found the derivative and then set the derivative to 0.\r<BR>\n" );
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document.write( "i used a derivative calculator to find the derivative.<BR>\n" );
document.write( "the derivative was equal to 1/sqrt(10 + 2x) - .1<BR>\n" );
document.write( "i set it to 0 and solved for x.<BR>\n" );
document.write( "i got x = 45.<BR>\n" );
document.write( "that's the same as i got using the graph.\r<BR>\n" );
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document.write( "either way, your maximum profit is at h = 45.<BR>\n" );
document.write( "at that point, f(h) = (10 + 2 * 45) ^ 1/2) - .1 * 45 = 5.5.\r<BR>\n" );
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document.write( "that means that the greatest profit is 5.5 thousand tanzanian shillings when the tree is 45 meters high.\r<BR>\n" );
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document.write( "let me know if you have any questions.<BR>\n" );
document.write( "theo\r<BR>\n" );
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