document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=147166>Question 147166</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I was given this problem and am not sure how to determine the answers. Could you please help? <BR>\n" );
document.write( "\"the production department of an electronics company projects the following costs to manufacture a new line of calculators marketing estimates the best retail price for the calculator is $92.\" <BR>\n" );
document.write( "# of calculators cost to produce x calculators<BR>\n" );
document.write( "0 $92,000<BR>\n" );
document.write( "10 84,200<BR>\n" );
document.write( "100 32,000 <BR>\n" );
document.write( "assuming this relationship is quadratic, find the quadratic function C(x)=ax^2+bx+c: I was given this problem and am not sure how to set up the quadratic formula. Could you please help? <BR>\n" );
document.write( "\"the production department of an electronics company projects the following costs to manufacture a new line of calculators marketing estimates the best retail price for the calculator is $92.\" <BR>\n" );
document.write( "# of calculators cost to produce x calculators<BR>\n" );
document.write( "0 $92,000<BR>\n" );
document.write( "10 84,200<BR>\n" );
document.write( "100 32,000 \r<BR>\n" );
document.write( "\n" );
document.write( "1) assuming this relationship is quadratic, find the quadratic function C(x)=ax^2+bx+c<BR>\n" );
document.write( "2) how many calculators must be sold to make this line of calculators profitable (what values of x make profit positive)? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #107550 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=107550\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \"the production department of an electronics company projects the following costs to manufacture a new line of calculators marketing estimates the best retail price for the calculator is $92.\" <BR>\n" );
document.write( "# of calculators cost to produce x calculators<BR>\n" );
document.write( "0 $92,000<BR>\n" );
document.write( "10 84,200<BR>\n" );
document.write( "100 32,000 <BR>\n" );
document.write( "1) assuming this relationship is quadratic, find the quadratic function <BR>\n" );
document.write( "C(x)=ax^2+bx+c<BR>\n" );
document.write( "----<BR>\n" );
document.write( "I don't have a calculator with me to do it but this is what you need to do:<BR>\n" );
document.write( "Substitute the \"point values into the quadratic for to get three equations<BR>\n" );
document.write( "in variables a, b, and c:<BR>\n" );
document.write( "92000 = a*0^2 + b*0 + c<BR>\n" );
document.write( "84200 = a*10^2 + b*10 + c<BR>\n" );
document.write( "32000 = a*100^2 + 100b + c<BR>\n" );
document.write( "--------------<BR>\n" );
document.write( "Solve this system of three equations for a, b, c<BR>\n" );
document.write( "--------------<BR>\n" );
document.write( "Write the equation.<BR>\n" );
document.write( "-------------------------<BR>\n" );
document.write( "2) how many calculators must be sold to make this line of calculators profitable (what values of x make profit positive)?<BR>\n" );
document.write( "Solve ax^2 + bx + c > 0<BR>\n" );
document.write( "===========================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );