document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=208178>Question 208178</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1. A company finds that it can produce 10 solar heaters for $7500 while the production of 20 heaters costs $13,900. If cost is a linear function of the number of heaters produced, express the cost function C(x) where x is the number of heaters produced. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #157497 by </B><A HREF=/tutors/aboutme.mpl?userid=nerdybill><B>nerdybill(7384)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=nerdybill><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=nerdybill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=157497\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">     1. A company finds that it can produce 10 solar heaters for $7500 while the production of 20 heaters costs $13,900. If cost is a linear function of the number of heaters produced, express the cost function C(x) where x is the number of heaters produced.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "The problem gives you two points in the equation:<BR>\n" );
document.write( "(10,7500)<BR>\n" );
document.write( "(20,13900)<BR>\n" );
document.write( ".<BR>\n" );
document.write( "And, since they said it was \"linear\" it fits the \"slope-intercept\" form<BR>\n" );
document.write( "y = mx + b<BR>\n" );
document.write( ".<BR>\n" );
document.write( "7500 = m(10) + b<BR>\n" );
document.write( "13900 = m(20) + b<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Rewriting the two equations:<BR>\n" );
document.write( "7500 = 10m + b<BR>\n" );
document.write( "13900 = 20m + b<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Applying the \"addition method\" we multiply the top equation by -1 and add:<BR>\n" );
document.write( " -7500 = -10m - b<BR>\n" );
document.write( "13900 = 20m + b<BR>\n" );
document.write( "-------------------<BR>\n" );
document.write( "6400 = 10m<BR>\n" );
document.write( "640 = m<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Using the top equation and the definition of m above:<BR>\n" );
document.write( "7500 = 10(640) + b<BR>\n" );
document.write( "7500 = 6400 + b<BR>\n" );
document.write( "1100 = b<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Pulling it back together we have:<BR>\n" );
document.write( "y = 640x + 1100<BR>\n" );
document.write( "or<BR>\n" );
document.write( "C(x) = 640x + 1100 (this is what they're looking for)<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );