document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=254800>Question 254800</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Manager has found that the cost to produce 100 cups of coffee is 11.02 and the cost to produce 400 cups of coffee is 40.12. Assume the C(x) is a linear function of x, find a formula for C(x).  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #187136 by </B><A HREF=/tutors/aboutme.mpl?userid=vksarvepalli><B>vksarvepalli(154)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=vksarvepalli><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=vksarvepalli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=187136\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let C(x) is the cost to produce x cups of coffee and is given by\r<BR>\n" );
document.write( "\n" );
document.write( "C(x)=ax+b where a and b are constants (given C(x) is a linear function of x)\r<BR>\n" );
document.write( "\n" );
document.write( "now given x=100 and C(x)=11.02 =>  11.02=100a+b  ------1\r<BR>\n" );
document.write( "\n" );
document.write( "and       x=400 and C(x)=40.12 =>  40.12=400a+b -------2\r<BR>\n" );
document.write( "\n" );
document.write( "subtract eq 1 from eq 2 \r<BR>\n" );
document.write( "\n" );
document.write( "we get  29.1=300a\r<BR>\n" );
document.write( "\n" );
document.write( "so a=0.097\r<BR>\n" );
document.write( "\n" );
document.write( "put this value of a in eq 1\r<BR>\n" );
document.write( "\n" );
document.write( "we get 11.02=9.7+b\r<BR>\n" );
document.write( "\n" );
document.write( "so b=1.32\r<BR>\n" );
document.write( "\n" );
document.write( "so the function is C(x)=0.097x+1.32 </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );