document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=464081>Question 464081</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me to solve this problem. In his model for storage and shipping costs of materials for a manufacturing process, Lancaster derives the cost function : <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%28k%29=100%28100%2B9k%2B144%2Fk%29 ALIGN=MIDDLE  ALT=\"C%28k%29=100%28100%2B9k%2B144%2Fk%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, 1 &#8804; k &#8804; 100 , where C(k) is the total cost (in dollars) of storage and transportation for 100 days of operation if a load of k tons of material is moved every k days. Find C(1). For what value of k does C(k) have a minimum ? what is the minimum value ? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #317875 by </B><A HREF=/tutors/aboutme.mpl?userid=robertb><B>robertb(5830)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=robertb><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=robertb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=317875\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> C(1) = 100(100 + 9 + 144) = 25,300 $ total cost of storage and transportation.\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%28k%29=100%28100%2B9k%2B144%2Fk%29 ALIGN=MIDDLE  ALT=\"C%28k%29=100%28100%2B9k%2B144%2Fk%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dC%28k%29%2Fdk+=+100%289-144%2Fk%5E2%29 ALIGN=MIDDLE  ALT=\"dC%28k%29%2Fdk+=+100%289-144%2Fk%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
document.write( "\n" );
document.write( "Setting the derivative equal to 0,<BR>\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+100%289-144%2Fk%5E2%29+=+0 ALIGN=MIDDLE  ALT=\"+100%289-144%2Fk%5E2%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > ==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9+-+144%2Fk%5E2+=+0 ALIGN=MIDDLE  ALT=\"9+-+144%2Fk%5E2+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > ==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9+=+144%2Fk%5E2 ALIGN=MIDDLE  ALT=\"9+=+144%2Fk%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k%5E2+=+144%2F9 ALIGN=MIDDLE  ALT=\"k%5E2+=+144%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" >  ==> k = 4.\r<BR>\n" );
document.write( "\n" );
document.write( "Now <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+d%5E2C%28k%29%2Fdk%5E2+=+100%28288%2Fk%5E3%29+%3E+0 ALIGN=MIDDLE  ALT=\"+d%5E2C%28k%29%2Fdk%5E2+=+100%28288%2Fk%5E3%29+%3E+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > when k = 4.\r<BR>\n" );
document.write( "\n" );
document.write( "==> Absolute minimum at k = 4.  \r<BR>\n" );
document.write( "\n" );
document.write( "Minimum value is C(4) = 100(100 + 9*4 + 144/4) = 17,200 $.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );