document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=90296>Question 90296</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0072549017/algebrahomeworkh>Beginning Al</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> The demand equation for a certain type of printer is given by:<BR>\n" );
document.write( "D = -200p + 35,000<BR>\n" );
document.write( "The supply equation is predicted to be<BR>\n" );
document.write( "S = -p^2 + 400p - 20,000<BR>\n" );
document.write( "Find the equilibrium price.\r<BR>\n" );
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document.write( "No clue on what to do...help is appreciated! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #65547 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=65547\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> To find the equilibrium price, set D equal to S\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-200p%2B35000=-p%5E2+%2B+400p+-+20000 ALIGN=MIDDLE  ALT=\"-200p%2B35000=-p%5E2+%2B+400p+-+20000\"   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=-200p%2B35000%2Bp%5E2=400p-20000 ALIGN=MIDDLE  ALT=\"-200p%2B35000%2Bp%5E2=400p-20000\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%5E2 ALIGN=MIDDLE  ALT=\"p%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-200p%2B35000%2Bp%5E2-400p=-20000 ALIGN=MIDDLE  ALT=\"-200p%2B35000%2Bp%5E2-400p=-20000\"   DISABLED_style= \"max-width:90%; height:auto;\" >Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=400p ALIGN=MIDDLE  ALT=\"400p\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-200p%2B35000%2Bp%5E2-400p%2B20000=0 ALIGN=MIDDLE  ALT=\"-200p%2B35000%2Bp%5E2-400p%2B20000=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20000 ALIGN=MIDDLE  ALT=\"20000\"   DISABLED_style= \"max-width:90%; height:auto;\" > to both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%5E2-600p%2B55000=0 ALIGN=MIDDLE  ALT=\"p%5E2-600p%2B55000=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms\r<BR>\n" );
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document.write( "Now let's use the quadratic formula to solve for p:\r<BR>\n" );
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document.write( "Starting with the general quadratic\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ap%5E2%2Bbp%2Bc=0 ALIGN=MIDDLE  ALT=\"ap%5E2%2Bbp%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "the general solution using the quadratic equation is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29 ALIGN=MIDDLE  ALT=\"p+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So lets solve <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%5E2-600%2Ap%2B55000=0 ALIGN=MIDDLE  ALT=\"p%5E2-600%2Ap%2B55000=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > ( notice <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=1 ALIGN=MIDDLE  ALT=\"a=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=-600 ALIGN=MIDDLE  ALT=\"b=-600\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=55000 ALIGN=MIDDLE  ALT=\"c=55000\"   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+=+%28--600+%2B-+sqrt%28+%28-600%29%5E2-4%2A1%2A55000+%29%29%2F%282%2A1%29 ALIGN=MIDDLE  ALT=\"p+=+%28--600+%2B-+sqrt%28+%28-600%29%5E2-4%2A1%2A55000+%29%29%2F%282%2A1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in a=1, b=-600, and c=55000\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p+=+%28600+%2B-+sqrt%28+%28-600%29%5E2-4%2A1%2A55000+%29%29%2F%282%2A1%29 ALIGN=MIDDLE  ALT=\"p+=+%28600+%2B-+sqrt%28+%28-600%29%5E2-4%2A1%2A55000+%29%29%2F%282%2A1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Negate -600 to get 600\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p+=+%28600+%2B-+sqrt%28+360000-4%2A1%2A55000+%29%29%2F%282%2A1%29 ALIGN=MIDDLE  ALT=\"p+=+%28600+%2B-+sqrt%28+360000-4%2A1%2A55000+%29%29%2F%282%2A1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square -600 to get 360000\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p+=+%28600+%2B-+sqrt%28+360000%2B-220000+%29%29%2F%282%2A1%29 ALIGN=MIDDLE  ALT=\"p+=+%28600+%2B-+sqrt%28+360000%2B-220000+%29%29%2F%282%2A1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4%2A55000%2A1 ALIGN=MIDDLE  ALT=\"-4%2A55000%2A1\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-220000 ALIGN=MIDDLE  ALT=\"-220000\"   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+=+%28600+%2B-+sqrt%28+140000+%29%29%2F%282%2A1%29 ALIGN=MIDDLE  ALT=\"p+=+%28600+%2B-+sqrt%28+140000+%29%29%2F%282%2A1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms in the radicand (everything under the square root)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p+=+%28600+%2B-+100%2Asqrt%2814%29%29%2F%282%2A1%29 ALIGN=MIDDLE  ALT=\"p+=+%28600+%2B-+100%2Asqrt%2814%29%29%2F%282%2A1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify the square root\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p+=+%28600+%2B-+100%2Asqrt%2814%29%29%2F2 ALIGN=MIDDLE  ALT=\"p+=+%28600+%2B-+100%2Asqrt%2814%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply 2 and 1 to get 2\r<BR>\n" );
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document.write( "So now the expression breaks down into two parts\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p+=+%28600+%2B+100%2Asqrt%2814%29%29%2F2 ALIGN=MIDDLE  ALT=\"p+=+%28600+%2B+100%2Asqrt%2814%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p+=+%28600+-+100%2Asqrt%2814%29%29%2F2 ALIGN=MIDDLE  ALT=\"p+=+%28600+-+100%2Asqrt%2814%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "which split up to\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=%2B600%2F2%2B100%2Asqrt%2814%29%2F2 ALIGN=MIDDLE  ALT=\"p=%2B600%2F2%2B100%2Asqrt%2814%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=%2B600%2F2-100%2Asqrt%2814%29%2F2 ALIGN=MIDDLE  ALT=\"p=%2B600%2F2-100%2Asqrt%2814%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "and simplify to\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=300%2B50%2Asqrt%2814%29 ALIGN=MIDDLE  ALT=\"p=300%2B50%2Asqrt%2814%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=300-50%2Asqrt%2814%29 ALIGN=MIDDLE  ALT=\"p=300-50%2Asqrt%2814%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Which approximate to\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=487.082869338697 ALIGN=MIDDLE  ALT=\"p=487.082869338697\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=112.917130661303 ALIGN=MIDDLE  ALT=\"p=112.917130661303\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So our solutions are:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=487.082869338697 ALIGN=MIDDLE  ALT=\"p=487.082869338697\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=112.917130661303 ALIGN=MIDDLE  ALT=\"p=112.917130661303\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "However, since the first solution <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=487.082869338697 ALIGN=MIDDLE  ALT=\"x=487.082869338697\"   DISABLED_style= \"max-width:90%; height:auto;\" > produces a negative demand value, we must discard the first solution.\r<BR>\n" );
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document.write( "So the equilibrium price is $112.92<BR>\n" );
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