document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=253584>Question 253584</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The members of the Lincoln High School Prom Committee are trying to raise money for their senior prom. They plan to sell teddy bears. The senior advisor told them that the profit equation for their project is y= -0.1x^2+9x-50 where x is the price at which the teddy bears will be sold and y is the profit, in dollars. How much profit can the committee expect to make if they sell the teddy bears for $20 each? What price should they charge for the teddy bears to make maximum profit possible? \r<BR>\n" );
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document.write( "It is a word problem with 2 questions!<BR>\n" );
document.write( "I did the first one:<BR>\n" );
document.write( "y= -0.1(20)^2+9(20)-50<BR>\n" );
document.write( "=-40+180-50<BR>\n" );
document.write( "=90<BR>\n" );
document.write( "If the teddy bears were sold for 20 dollars each, they would make 90 dollars! \r<BR>\n" );
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document.write( "I don't understand the second problem:<BR>\n" );
document.write( "What price should they charge for the teddy bears to make maximum profit possible?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #185926 by </B><A HREF=/tutors/aboutme.mpl?userid=JimboP1977><B>JimboP1977(311)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=JimboP1977><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=JimboP1977><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=185926\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> They are asking you at what value x will give the largest value of y. Quadratics always produce a graph called a parabola. In this case the parabola is inverted (upside down) because the coefficient of x^2 is a minus number.\r<BR>\n" );
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document.write( "In essence, we need to find when the parabola peaks or when the gradient is zero.\r<BR>\n" );
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document.write( "We can do this by differentiation. dy/dx = -0.2x+9.This gives the gradient at any given value of x. We want the gradient to be zero so 0= -0.2x+9 so x = 45.\r<BR>\n" );
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document.write( "If we plot the graph of y= -0.1x^2+9x-50 we can see that this is true.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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