Question No:1 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 x miles over a 3-year period. (b) 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?
Answers
Given : 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
To Find : Formulate the total revenue function associated with renting one of the cars for a total of x miles over a 3 year period
Solution:
The car cost = $15,000
Fixed Cost = $15,000
Variable Cost = $0.18 per mile.
Cost for x Miles = 0.18x $
sold for $4,500. -
Fixed Revenue after 3 years = $4,500.
Cars are leased for a flat fee of $0.33 per mile
Variable Revenue = 0.33x $
Total Revenue = 0.33x + 4,500 $
Total Cost = 0.18x + 15,000 $
Profit = Revenue - Cost
= 0.33x + 4,500. - 0.18x - 15,000
= 0.15x - 10500 $
Break even point
0.15x - 10500 = 0
=> x = 70000
70000 miles is break-even point
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