document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1200730>Question 1200730</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The total cost,C,(in thousands of dollars) to make reading glasses is<BR>\n" );
document.write( "a function of the number of pairs of glasses made U(in thousands) and is given by C(u)= -0.02u^2 + 2.33u + 11.61\r<BR>\n" );
document.write( "\n" );
document.write( "a)Find the marginal cost at the production level of 21 thousand and choose the correct units\r<BR>\n" );
document.write( "\n" );
document.write( "b)What is the average cost at the same production level?<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #848062 by </B><A HREF=/tutors/aboutme.mpl?userid=GingerAle><B>GingerAle(43)</B></A><img src=\"/images/stars/stars-07.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=GingerAle><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=848062\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> **a) Find the Marginal Cost**\r<BR>\n" );
document.write( "\n" );
document.write( "1. **Find the derivative of the cost function:**<BR>\n" );
document.write( "   * C'(u) = d/du (-0.02u² + 2.33u + 11.61) <BR>\n" );
document.write( "   * C'(u) = -0.04u + 2.33\r<BR>\n" );
document.write( "\n" );
document.write( "2. **Evaluate the derivative at u = 21 (production level of 21 thousand pairs):**<BR>\n" );
document.write( "   * C'(21) = -0.04 * 21 + 2.33 <BR>\n" );
document.write( "   * C'(21) = 1.49\r<BR>\n" );
document.write( "\n" );
document.write( "**Therefore, the marginal cost at a production level of 21 thousand pairs of glasses is $1.49 thousand per thousand pairs (or $1490 per thousand pairs).**\r<BR>\n" );
document.write( "\n" );
document.write( "**b) Find the Average Cost**\r<BR>\n" );
document.write( "\n" );
document.write( "1. **Calculate the total cost at u = 21:**<BR>\n" );
document.write( "   * C(21) = -0.02 * (21)² + 2.33 * 21 + 11.61 <BR>\n" );
document.write( "   * C(21) = -8.82 + 48.93 + 11.61 <BR>\n" );
document.write( "   * C(21) = 51.72 thousand dollars\r<BR>\n" );
document.write( "\n" );
document.write( "2. **Calculate the average cost:**<BR>\n" );
document.write( "   * Average Cost = Total Cost / Number of Units<BR>\n" );
document.write( "   * Average Cost = 51.72 thousand dollars / 21 thousand pairs<BR>\n" );
document.write( "   * Average Cost = 2.46 dollars per pair\r<BR>\n" );
document.write( "\n" );
document.write( "**Therefore, the average cost at a production level of 21 thousand pairs of glasses is $2.46 per pair.**<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );