document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=33505>Question 33505</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0073016020/algebrahomeworkh></A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> 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. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #19919 by </B><A HREF=/tutors/aboutme.mpl?userid=mbarugel><B>mbarugel(146)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mbarugel><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=19919\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Hello!<BR>\n" );
document.write( "This question can be easily solved in the following way.\r<BR>\n" );
document.write( "\n" );
document.write( "We call \"equilibrium price\" to the the price (the value of \"p\") that makes demand equal supply. So we simply have to set up the equation:\r<BR>\n" );
document.write( "\n" );
document.write( "D = S\r<BR>\n" );
document.write( "\n" );
document.write( "Since:\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D=+-200p+%2B+35000 ALIGN=MIDDLE  ALT=\"D=+-200p+%2B+35000\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S=+-p%5E2+%2B+400p+-+20000 ALIGN=MIDDLE  ALT=\"S=+-p%5E2+%2B+400p+-+20000\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "Then, from D = S, we get:\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-200p+%2B+35000+=+-p%5E2+%2B+400p+-+20000 ALIGN=MIDDLE  ALT=\"-200p+%2B+35000+=+-p%5E2+%2B+400p+-+20000\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "After combining like terms, we're left with:\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-p%5E2+%2B+600p+-+55000+=+0 ALIGN=MIDDLE  ALT=\"-p%5E2+%2B+600p+-+55000+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "This quadratic equation can then be solved using the quadratic formula:\r<BR>\n" );
document.write( "\n" );
document.write( "<TABLE  BORDER=1>\n" );
document.write( "\n" );
document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=solve_quadratic_equation.solver>SOLVE quadratic equation (work shown, graph etc)</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Quadratic equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2%2Bbx%2Bc=0 ALIGN=MIDDLE  ALT=\"ax%5E2%2Bbx%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in our case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1x%5E2%2B600x%2B-55000+=+0 ALIGN=MIDDLE  ALT=\"-1x%5E2%2B600x%2B-55000+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >) has the following solutons:<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  For these solutions to exist, the <U>discriminant</U> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" > should not be a negative number.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  First, we need to compute the discriminant <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" >: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac=%28600%29%5E2-4%2A-1%2A-55000=140000 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28600%29%5E2-4%2A-1%2A-55000=140000\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=140000 is greater than zero. That means that there are two solutions: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5B12%5D+=+%28-600%2B-sqrt%28+140000+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-600%2B-sqrt%28+140000+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D+=+%28-%28600%29%2Bsqrt%28+140000+%29%29%2F2%5C-1+=+112.917130661303 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28600%29%2Bsqrt%28+140000+%29%29%2F2%5C-1+=+112.917130661303\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D+=+%28-%28600%29-sqrt%28+140000+%29%29%2F2%5C-1+=+487.082869338697 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28600%29-sqrt%28+140000+%29%29%2F2%5C-1+=+487.082869338697\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <BR>\n" );
document.write( "    Quadratic expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1x%5E2%2B600x%2B-55000 ALIGN=MIDDLE  ALT=\"-1x%5E2%2B600x%2B-55000\"   DISABLED_style= \"max-width:90%; height:auto;\" > can be factored:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1x%5E2%2B600x%2B-55000+=+%28x-112.917130661303%29%2A%28x-487.082869338697%29 ALIGN=MIDDLE  ALT=\"-1x%5E2%2B600x%2B-55000+=+%28x-112.917130661303%29%2A%28x-487.082869338697%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 112.917130661303, 487.082869338697.\n" );
document.write( "Here's your graph:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-1%2Ax%5E2%2B600%2Ax%2B-55000+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-1%2Ax%5E2%2B600%2Ax%2B-55000+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So there are two solutions: p=112.91 or p=487.08. However, notice that the 487.08 solution doesn't make sense, as supply and demand are negative in this case (try plugging p=487.08 into either the supply or demand formula). Therefore, the correct answer is that the equilibrium price is 112.91.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "I hope this helps!<BR>\n" );
document.write( "Get more answers at <a  rel=nofollow HREF=http://www.onlinemathanswers.com>Online Math Answers.com</a>! </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );