document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1072659>Question 1072659</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 2. Assume that the cost of fuel for a ship is proportional to the cube of velocity of the ship. When the velocity is 10 km/h the cost of fuel is $80 per hour, and other expenses for the ship are $480 per hour.<BR>\n" );
document.write( "What velocity of the ship minimizes the total expenses if the ship sails 20km?<BR>\n" );
document.write( "In this case what are the total expenses per hour?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #687508 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=687508\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 2. Assume that the cost of fuel for a ship is proportional to the cube of velocity of the ship.<BR>\n" );
document.write( " When the velocity is 10 km/h the cost of fuel is $80 per hour, and other expenses for the ship are $480 per hour.<BR>\n" );
document.write( "What velocity of the ship minimizes the total expenses if the ship sails 20km?<BR>\n" );
document.write( "In this case what are the total expenses per hour?<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Fuel cost equation<BR>\n" );
document.write( "v^3*k = cost/hr<BR>\n" );
document.write( "Using the given values<BR>\n" );
document.write( "10^3*k = 80<BR>\n" );
document.write( "1000k = 80<BR>\n" );
document.write( "k = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=80%2F1000 ALIGN=MIDDLE  ALT=\"80%2F1000\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "k = .08<BR>\n" );
document.write( "The hourly fuel cost expression = .08v^3<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Cost equation for a 20 km <BR>\n" );
document.write( "C(v) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20%2Fv ALIGN=MIDDLE  ALT=\"20%2Fv\"   DISABLED_style= \"max-width:90%; height:auto;\" >(.08v^3 + 480)<BR>\n" );
document.write( "graphically<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-6%2C+30%2C+-200%2C+2000%2C+%2820%2Fx%29%28.08x%5E3%2B480%29%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+200%2C+-6%2C+30%2C+-200%2C+2000%2C+%2820%2Fx%29%28.08x%5E3%2B480%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Minimum cost at a velocity of 14.4 km/hr<BR>\n" );
document.write( ":<BR>\n" );
document.write( "\"In this case what are the total expenses per hour?\"<BR>\n" );
document.write( ".08(14.4^3) = $238.87 per hr<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Cost for a 20 km trip<BR>\n" );
document.write( "C(v) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20%2F14.4 ALIGN=MIDDLE  ALT=\"20%2F14.4\"   DISABLED_style= \"max-width:90%; height:auto;\" >(.08*14.4^3 + 480)<BR>\n" );
document.write( "C(v) = $998.44<BR>\n" );
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