document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1184261>Question 1184261</A>: <I><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "Automobile Leasing A car leasing agency purchases new cars each year for use in the agency. The cars cost $15,000 new. They are used for 3 years, after which they are sold for $4,500. The owner of the agency estimates that the variable costs of operating the cars, exclusive of gasoline, are $0.18 per mile. Cars are leased for a flat fee of $0.33 per mile (gasoline not included). <BR>\n" );
document.write( "(a) Formulate the total revenue function associated with renting one of the cars a total of<BR>\n" );
document.write( "miles over a 3-year period. <BR>\n" );
document.write( "(6) Formulate the total cost function associated with renting a car for a total of x miles<BR>\n" );
document.write( "over 3 years<BR>\n" );
document.write( "(c) Formulate the profit function.<BR>\n" );
document.write( "(d) What is profit if a car is leased for 60,000 miles over a 3-year period? <BR>\n" );
document.write( "(e) What mileage is required in order to earn zero profit for 3 years? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #814794 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=814794\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the cars cost 15000 when they are new.<BR>\n" );
document.write( "they are used for 3 years.<BR>\n" );
document.write( "at the end of the 3 years, they are sold for 4500.\r<BR>\n" );
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document.write( "the variable cost for operating the cars is .18 per mile, exclusive of gas.\r<BR>\n" );
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document.write( "the cars are leased for .33 per mile.\r<BR>\n" );
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document.write( "the cost to the rental agency for operating and leasing the car for 3 years is equal to (15000 - 4500) = 10500 + .18 * x, where x is the number of miles the car was used during the lease period.\r<BR>\n" );
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document.write( "the revenue to the rental agency that lease the car was .33 * x, where x is the number of miles the car was used during the lease period.\r<BR>\n" );
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document.write( "profit = revenue minus cost = .33 * x - 10500 - .18 * x = .15 * x - 10500.\r<BR>\n" );
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document.write( "if the car is operated for 60000 miles, then the formula becomes profit = .15 * 60000 - 10500 = -1500 dollars.\r<BR>\n" );
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document.write( "to break even, the formula becomes 0 = .15 * x - 10500.<BR>\n" );
document.write( "add 10500 to both sides of this equation to get 10500 = .15 * x<BR>\n" );
document.write( "solve for x to get:<BR>\n" );
document.write( "x = 10500 / .15 = 70000.<BR>\n" );
document.write( "that's the number of miles in a 3 year period that the car needs to be operated so that the rental agency can break even.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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