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 #185927 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=185927\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The max profit occurs at the vertex since the vertex represents the max value of y.\r<BR>\n" );
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document.write( "In order to find the vertex, we first need to find the x-coordinate of the vertex.\r<BR>\n" );
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document.write( "To find the x-coordinate of the vertex, use this formula: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28-b%29%2F%282a%29 ALIGN=MIDDLE  ALT=\"x=%28-b%29%2F%282a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28-b%29%2F%282a%29 ALIGN=MIDDLE  ALT=\"x=%28-b%29%2F%282a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given formula.\r<BR>\n" );
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document.write( "From <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-0.1x%5E2%2B9x-50 ALIGN=MIDDLE  ALT=\"y=-0.1x%5E2%2B9x-50\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we can see that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=-0.1 ALIGN=MIDDLE  ALT=\"a=-0.1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=9 ALIGN=MIDDLE  ALT=\"b=9\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=-50 ALIGN=MIDDLE  ALT=\"c=-50\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28-%289%29%29%2F%282%28-0.1%29%29 ALIGN=MIDDLE  ALT=\"x=%28-%289%29%29%2F%282%28-0.1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=-0.1 ALIGN=MIDDLE  ALT=\"a=-0.1\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=9 ALIGN=MIDDLE  ALT=\"b=9\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28-9%29%2F%28-0.2%29 ALIGN=MIDDLE  ALT=\"x=%28-9%29%2F%28-0.2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply 2 and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-0.1 ALIGN=MIDDLE  ALT=\"-0.1\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-0.2 ALIGN=MIDDLE  ALT=\"-0.2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=45 ALIGN=MIDDLE  ALT=\"x=45\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide.\r<BR>\n" );
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document.write( "So the x-coordinate of the vertex is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=45 ALIGN=MIDDLE  ALT=\"x=45\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Note: this means that the axis of symmetry is also <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=45 ALIGN=MIDDLE  ALT=\"x=45\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Now that we know the x-coordinate of the vertex, we can use it to find the y-coordinate of the vertex.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-0.1x%5E2%2B9x-50 ALIGN=MIDDLE  ALT=\"y=-0.1x%5E2%2B9x-50\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-0.1%2845%29%5E2%2B9%2845%29-50 ALIGN=MIDDLE  ALT=\"y=-0.1%2845%29%5E2%2B9%2845%29-50\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=45 ALIGN=MIDDLE  ALT=\"x=45\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-0.1%282025%29%2B9%2845%29-50 ALIGN=MIDDLE  ALT=\"y=-0.1%282025%29%2B9%2845%29-50\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=45 ALIGN=MIDDLE  ALT=\"45\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2025 ALIGN=MIDDLE  ALT=\"2025\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-202.5%2B9%2845%29-50 ALIGN=MIDDLE  ALT=\"y=-202.5%2B9%2845%29-50\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-0.1 ALIGN=MIDDLE  ALT=\"-0.1\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2025 ALIGN=MIDDLE  ALT=\"2025\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-202.5 ALIGN=MIDDLE  ALT=\"-202.5\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-202.5%2B405-50 ALIGN=MIDDLE  ALT=\"y=-202.5%2B405-50\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9 ALIGN=MIDDLE  ALT=\"9\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=45 ALIGN=MIDDLE  ALT=\"45\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=405 ALIGN=MIDDLE  ALT=\"405\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=152.5 ALIGN=MIDDLE  ALT=\"y=152.5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms.\r<BR>\n" );
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document.write( "So the y-coordinate of the vertex is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=152.5 ALIGN=MIDDLE  ALT=\"y=152.5\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "So the vertex is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(45,152.5\right)\">.\r<BR>\n" );
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document.write( "Since the vertex represents the max value of y, and y is the profit, this means that the max profit is $152.50 (since the y value of the vertex is y=152.5)\r<BR>\n" );
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document.write( "This profit is attained when the price is $45 (since the x coordinate of the vertex is x=45) </SPAN>\n" );
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