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Question 1184261:
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).
(a) Formulate the total revenue function associated with renting one of the cars a total of
miles over a 3-year period.
(6) Formulate the total cost function associated with renting a car for a total of x miles
over 3 years
(c) Formulate the profit function.
(d) What is profit if a car is leased for 60,000 miles over a 3-year period?
(e) What mileage is required in order to earn zero profit for 3 years?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the cars cost 15000 when they are new.
they are used for 3 years.
at the end of the 3 years, they are sold for 4500.
the variable cost for operating the cars is .18 per mile, exclusive of gas.
the cars are leased for .33 per mile.
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.
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.
profit = revenue minus cost = .33 * x - 10500 - .18 * x = .15 * x - 10500.
if the car is operated for 60000 miles, then the formula becomes profit = .15 * 60000 - 10500 = -1500 dollars.
to break even, the formula becomes 0 = .15 * x - 10500.
add 10500 to both sides of this equation to get 10500 = .15 * x
solve for x to get:
x = 10500 / .15 = 70000.
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.
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