document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=153209>Question 153209</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can someone help me out, please? Thank you!\r<BR>\n" );
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document.write( "The owners of a parking garage have determined that their weekly revenue and cost in dollars are given by the following:\r<BR>\n" );
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document.write( "R(x) = 56x - 2x^2<BR>\n" );
document.write( "C(x) = 24x + 101\r<BR>\n" );
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document.write( "find the break even point. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #112727 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=112727\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Remember, \r<BR>\n" );
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document.write( "Profit =  Revenue - Cost\r<BR>\n" );
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document.write( "which is symbolically:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28x%29=R%28x%29-C%28x%29 ALIGN=MIDDLE  ALT=\"P%28x%29=R%28x%29-C%28x%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=P%28x%29=%2856x+-+2x%5E2%29-%2824x+%2B+101%29 ALIGN=MIDDLE  ALT=\"P%28x%29=%2856x+-+2x%5E2%29-%2824x+%2B+101%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%28x%29+=+56x+-+2x%5E2 ALIGN=MIDDLE  ALT=\"R%28x%29+=+56x+-+2x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%28x%29+=+24x+%2B+101+ ALIGN=MIDDLE  ALT=\"C%28x%29+=+24x+%2B+101+\"   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=P%28x%29=56x+-+2x%5E2-24x+-+101 ALIGN=MIDDLE  ALT=\"P%28x%29=56x+-+2x%5E2-24x+-+101\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute the negative.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28x%29=-2x%5E2%2B32x-101 ALIGN=MIDDLE  ALT=\"P%28x%29=-2x%5E2%2B32x-101\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms\r<BR>\n" );
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document.write( "Now the break even point occurs when you neither gain money nor lose money. In other words, break even point happens when the profit is zero. So this means that the break even point occurs when <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28x%29=0 ALIGN=MIDDLE  ALT=\"P%28x%29=0\"   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=0=-2x%5E2%2B32x-101 ALIGN=MIDDLE  ALT=\"0=-2x%5E2%2B32x-101\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28x%29=0 ALIGN=MIDDLE  ALT=\"P%28x%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Notice we have a quadratic equation in the form of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2%2Bbx%2Bc ALIGN=MIDDLE  ALT=\"ax%5E2%2Bbx%2Bc\"   DISABLED_style= \"max-width:90%; height:auto;\" > where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=-2 ALIGN=MIDDLE  ALT=\"a=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=32 ALIGN=MIDDLE  ALT=\"b=32\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=-101 ALIGN=MIDDLE  ALT=\"c=-101\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Let's use the quadratic formula to solve for x\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29 ALIGN=MIDDLE  ALT=\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the quadratic formula\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-%2832%29+%2B-+sqrt%28+%2832%29%5E2-4%28-2%29%28-101%29+%29%29%2F%282%28-2%29%29 ALIGN=MIDDLE  ALT=\"x+=+%28-%2832%29+%2B-+sqrt%28+%2832%29%5E2-4%28-2%29%28-101%29+%29%29%2F%282%28-2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=-2 ALIGN=MIDDLE  ALT=\"a=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=32 ALIGN=MIDDLE  ALT=\"b=32\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=-101 ALIGN=MIDDLE  ALT=\"c=-101\"   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+=+%28-32+%2B-+sqrt%28+1024-4%28-2%29%28-101%29+%29%29%2F%282%28-2%29%29 ALIGN=MIDDLE  ALT=\"x+=+%28-32+%2B-+sqrt%28+1024-4%28-2%29%28-101%29+%29%29%2F%282%28-2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=32 ALIGN=MIDDLE  ALT=\"32\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1024 ALIGN=MIDDLE  ALT=\"1024\"   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+=+%28-32+%2B-+sqrt%28+1024-808+%29%29%2F%282%28-2%29%29 ALIGN=MIDDLE  ALT=\"x+=+%28-32+%2B-+sqrt%28+1024-808+%29%29%2F%282%28-2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%28-2%29%28-101%29 ALIGN=MIDDLE  ALT=\"4%28-2%29%28-101%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=808 ALIGN=MIDDLE  ALT=\"808\"   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+=+%28-32+%2B-+sqrt%28+216+%29%29%2F%282%28-2%29%29 ALIGN=MIDDLE  ALT=\"x+=+%28-32+%2B-+sqrt%28+216+%29%29%2F%282%28-2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=808 ALIGN=MIDDLE  ALT=\"808\"   DISABLED_style= \"max-width:90%; height:auto;\" > from <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1024 ALIGN=MIDDLE  ALT=\"1024\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=216 ALIGN=MIDDLE  ALT=\"216\"   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+=+%28-32+%2B-+sqrt%28+216+%29%29%2F%28-4%29 ALIGN=MIDDLE  ALT=\"x+=+%28-32+%2B-+sqrt%28+216+%29%29%2F%28-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2 ALIGN=MIDDLE  ALT=\"-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4 ALIGN=MIDDLE  ALT=\"-4\"   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+=+%28-32+%2B-+6%2Asqrt%286%29%29%2F%28-4%29 ALIGN=MIDDLE  ALT=\"x+=+%28-32+%2B-+6%2Asqrt%286%29%29%2F%28-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify the square root  (note: If you need help with simplifying square roots, check out this <a  rel=nofollow HREF=http://www.algebra.com/algebra/homework/Radicals/simplifying-square-roots.solver> solver</a>)  \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-32%2B6%2Asqrt%286%29%29%2F%28-4%29 ALIGN=MIDDLE  ALT=\"x+=+%28-32%2B6%2Asqrt%286%29%29%2F%28-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-32-6%2Asqrt%286%29%29%2F%28-4%29 ALIGN=MIDDLE  ALT=\"x+=+%28-32-6%2Asqrt%286%29%29%2F%28-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Break up the expression.  \r<BR>\n" );
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document.write( "So the answers are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-32%2B6%2Asqrt%286%29%29%2F%28-4%29 ALIGN=MIDDLE  ALT=\"x+=+%28-32%2B6%2Asqrt%286%29%29%2F%28-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-32-6%2Asqrt%286%29%29%2F%28-4%29 ALIGN=MIDDLE  ALT=\"x+=+%28-32-6%2Asqrt%286%29%29%2F%28-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "which approximate to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=4.33 ALIGN=MIDDLE  ALT=\"x=4.33\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=11.67 ALIGN=MIDDLE  ALT=\"x=11.67\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "So the break even points occur when the price is either $4.33 or $11.67 </SPAN>\n" );
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