document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=180862>Question 180862</A>: <I><SPAN STYLE=\"word-break: break-all;\"> With a 12 gallon tank, a Jupiter gets 22 mi/gal.  Engineers estimate that every 2 gallon increase in tank size causes gas mileage to decrease by 1 mi/gal.  What should the size of the tank be for the Jupiter to have the greatest range (number of miles on a tank of gas)?<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 #135606 by </B><A HREF=/tutors/aboutme.mpl?userid=kev82><B>kev82(151)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=kev82><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=135606\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> v = volume of tank<BR>\n" );
document.write( "r = miles per gallon\r<BR>\n" );
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document.write( "distance = vr\r<BR>\n" );
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document.write( "dr/dv = -0.5  (every increase of 2 decreases by 1)\r<BR>\n" );
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document.write( "r = c - 0.5v (integrate)\r<BR>\n" );
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document.write( "22 = c - 6 (substitute r=22,v=12)\r<BR>\n" );
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document.write( "c = 28\r<BR>\n" );
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document.write( "v(28-0.5v) = distance (substitute)\r<BR>\n" );
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document.write( "28-0.5v -0.5v = 28-v = 0 (differentiate and solve for turning point)\r<BR>\n" );
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document.write( "v = 28 \r<BR>\n" );
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document.write( "r = 28 - 14 = 14 (calculate r at turning point)\r<BR>\n" );
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document.write( "14*28 = 392 (calculate distance) </SPAN>\n" );
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