document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=548215>Question 548215</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A shopkeeper finds that the cost C of ordering and storing the latest laptop is<BR>\n" );
document.write( "C = 2 x + (300000 / x), where x is in the interval [1, 300]. The delivery of truck can bring at most 300 units per<BR>\n" );
document.write( "order.<BR>\n" );
document.write( "(a) Find the order size that will minimize the cost<BR>\n" );
document.write( "(b) Could the cost be decreased if the truck is replaced with a larger one that could bring 400 units? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #356820 by </B><A HREF=/tutors/aboutme.mpl?userid=htmentor><B>htmentor(1343)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=htmentor><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=htmentor><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=356820\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A shopkeeper finds that the cost C of ordering and storing the latest laptop is<BR>\n" );
document.write( "C = 2 x + (300000 / x), where x is in the interval [1, 300]. The delivery of truck can bring at most 300 units per<BR>\n" );
document.write( "order.<BR>\n" );
document.write( "(a) Find the order size that will minimize the cost<BR>\n" );
document.write( "(b) Could the cost be decreased if the truck is replaced with a larger one that could bring 400 units?<BR>\n" );
document.write( "=====================================<BR>\n" );
document.write( "The minimum of the cost function is obtained by taking the derivative and setting=0<BR>\n" );
document.write( "C(x) = 2x + 300000/x<BR>\n" );
document.write( "dC(x)/dx = 0 = 2 - 300000/x^2<BR>\n" );
document.write( "Divide through by 2, multiply through by x^2:<BR>\n" );
document.write( "0 = x^2 - 150000<BR>\n" );
document.write( "Taking the positive solution, we get x = sqrt(150000) = 387 [to the nearest unit]<BR>\n" );
document.write( "(a) However, the truck can deliver at most 300 units. Therefore, the order size which will minimize the cost is 300 units.<BR>\n" );
document.write( "(b) Yes. The cost is minimized when the number of units is 387 </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );