document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1042307>Question 1042307</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A firm's fixed cost is $50,000, the cost of making 10,000 units of its product is $100,000 and the cost of making 20,000 units is $250,000. Find the firm's cost function if it is known to be quadratic. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #657828 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=657828\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> it took some doing, but i think i found the answer.<BR>\n" );
document.write( "the answer is y = .0005 * x^2 + 50,000\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the graph of that equation looks like this:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2016/073102.jpg\" alt=\"$$$\" </>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the procedure is as follows:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the general form of a quadratic equation is:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "y = ax^2 + bx + c\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "when y = 100,000 and x = 10,000, and c = 50,000, the equation becomes:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "100,000 = 10,000^2 * a + 10,000 * b + 50,000\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "when y = 250,000 and x = 20,000, and c = 50,000, the equation becomes:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "250,000 = 20,000^2 * a + 20,000 * b + 50,000\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "subtract 50,000 from both sides of each equation and you get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "50,000 = 10,000^2 * a + 10,000 * b<BR>\n" );
document.write( "200,000 = 20,000^2 * a + 20,000 * b\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "multiply both sides of the first equation by 2 and you get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "100,000 = 2 * 10,000^2 * a + 2 * 10,000 * b<BR>\n" );
document.write( "200,000 = 20,000^2 + a + 20,000 * b\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "simplify the first equation and leave the second equation as is to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "100,000 = 2 * 10,000^2 * a + 20,000 * b<BR>\n" );
document.write( "200,000 = 20,000^2 * a + 20,000 * b\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "subtract the first equation from the second equation to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "100,000 = 20,000^2 * a - 2 * 10,000^2 * a\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "simplify to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "100,000 = 200,000,000 * a\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "divide both sides of the equation by 200,000,000 to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "100,000 / 200,000,000 = a\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "solve for a to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "a = .0005\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "go back to the first original equation of 50,000 = 10,000^2 * a + 10,000 * b and replace a with .0005 and solve for b to get b = 0.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you have a = .0005 and b = 0 and c = 50,000\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the general equation of y = ax^2 + bx + c becomes:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "y = .0005x^2 + 0x + 50,000 which becomes:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "y = .0005x^2 + 50,000\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );