document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=150353>Question 150353</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0073268623/algebrahomeworkh></A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Minimizing cost. A company uses the formula C(x) = 0.02x² - 3.4x + 150 to model the unit cost in dollars for producing x stabilizer bars. For what number of bars is the unit cost at its minimum? What is the unit cost at that level of production? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #110298 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=110298\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Minimizing cost. A company uses the formula C(x) = 0.02x² - 3.4x + 150 to model the unit cost in dollars for producing x stabilizer bars. For what number of bars is the unit cost at its minimum? What is the unit cost at that level of production?<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Simply by looking at a quadratic equation we can tell whether opens up or down.  If it opens down -- the vertex gives you the maximum.  If it opens up -- the vertex gives you a minimum.<BR>\n" );
document.write( "To do this, consider the general quadratic form:<BR>\n" );
document.write( "y = ax^2 + bx + c<BR>\n" );
document.write( "You simply need to look at the coefficient of the x^2 term (a) -- if it is positive, it opens up.  if it is negative, it opens down.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Looking at:<BR>\n" );
document.write( "C(x) = 0.02x² - 3.4x + 150 <BR>\n" );
document.write( "the value of 'a' is 0.02 (positive) therefore, the vertex will be a \"minimum\".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "The x coordinate of the vertex can be found with:<BR>\n" );
document.write( "x = -b/2a<BR>\n" );
document.write( "x = -(-3.4)/2(.02)<BR>\n" );
document.write( "x = (3.4)/(.04)<BR>\n" );
document.write( "x = 85<BR>\n" );
document.write( ".<BR>\n" );
document.write( "For what number of bars is the unit cost at its minimum? 85 stabilizer bars <BR>\n" );
document.write( ".<BR>\n" );
document.write( "C(x) = 0.02x² - 3.4x + 150 <BR>\n" );
document.write( "C(85) = 0.02(85)² - 3.4(85) + 150 <BR>\n" );
document.write( "C(85) = 144.5 - 289 + 150 <BR>\n" );
document.write( "C(85) = 5.5<BR>\n" );
document.write( ".<BR>\n" );
document.write( "What is the unit cost at that level of production? $5.50<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );