document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=215071>Question 215071</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I'm having trouble setting up this question, help would be appreciated:<BR>\n" );
document.write( "Research has shown that if 100 pear trees are planted, then the annual revenue is $90 per tree.  If more trees are planted they have less room to grow and generate fewer pears per tree.  As a result, the annual revenue per free is reduced $0.70 for each additional tree planted.  No matter how many trees are plated, the cost of maintaining each tree is $7.40 per year. How many pear trees should be planted to maximize the profit from the orchard for one year?\r<BR>\n" );
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document.write( "Let 'x' represent the amount of pear trees planted.<BR>\n" );
document.write( "Profit = Revenue - Cost<BR>\n" );
document.write( "Revenue = (90-0.7x)(100+x)<BR>\n" );
document.write( "Cost = 7.40(100+x)<BR>\n" );
document.write( "Profit = 9000+90x-70x-0.7x^2-740+7.4x<BR>\n" );
document.write( "The function I work out is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-0.7x%5E2%2B27.4x%2B8260+ ALIGN=MIDDLE  ALT=\"+-0.7x%5E2%2B27.4x%2B8260+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "However I can't work it out correctly, can someone help me set this problem up??  Thanks in advance. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #162571 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=162571\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Research has shown that if 100 pear trees are planted, then the annual revenue is $90 per tree.<BR>\n" );
document.write( " If more trees are planted they have less room to grow and generate fewer pears per tree.<BR>\n" );
document.write( " As a result, the annual revenue per tree is reduced $0.70 for each additional tree planted.<BR>\n" );
document.write( " No matter how many trees are planted, the cost of maintaining each tree is $7.40 per year. <BR>\n" );
document.write( "How many pear trees should be planted to maximize the profit from the orchard for one year?<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Let 'x' represent the amount of pear trees planted.<BR>\n" );
document.write( "Profit = Revenue - Cost<BR>\n" );
document.write( "Revenue = (90-0.7x)(100+x)<BR>\n" );
document.write( "Cost = 7.40(100+x)<BR>\n" );
document.write( "Right here I think you made a mistake<BR>\n" );
document.write( "Profit = 9000 + 90x - 70x - 0.7x^2 - 7.40(100 + x)<BR>\n" );
document.write( "which is<BR>\n" );
document.write( "Profit = 9000 + 90x - 70x - 0.7x^2 - 740 - 7.4x; (you had +7.4x}<BR>\n" );
document.write( "Profit = 9000 + 20x - 0.7x^2 - 740 - 7.4x;<BR>\n" );
document.write( "Profit = 9000 - 740 + 20x - 7.4x - 0.7x^2 <BR>\n" );
document.write( ":<BR>\n" );
document.write( "So you would have\r<BR>\n" );
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document.write( "-0.7x^2  +  12.6x + 8260<BR>\n" );
document.write( ":<BR>\n" );
document.write( "A quadratic equation so we can find the axis of symmetry of x for max profit<BR>\n" );
document.write( "x = -b/(2a)<BR>\n" );
document.write( "in this equation a = -.7; b = 12.6.<BR>\n" );
document.write( "x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-12.6%29%2F%282%2A-.7%29 ALIGN=MIDDLE  ALT=\"%28-12.6%29%2F%282%2A-.7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-12.6%29%2F%28-1.4%29 ALIGN=MIDDLE  ALT=\"%28-12.6%29%2F%28-1.4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = 9 more trees, making it 109 trees for max profit<BR>\n" );
document.write( ":<BR>\n" );
document.write( ":<BR>\n" );
document.write( "You certainly had the right idea, just a little sign error. </SPAN>\n" );
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