A car leasing agency purchases new cars each year for use in the agency. The cars cost $15000 new. They are used for 3 years, after which they are sold for $3600. The owner of the agency estimates that the variable costs of operating the cars, exclusive gasoline, are $0.16 per mile. Cars are leased at a flat rate of $0.33 per mile (gasoline not included). a. What is the break even mileage for three years period? b. What are total revenue, total cost, and total profit for the three year period if a car is leased for 50000 miles? c. What price per mile must be charged in order to breakeven if a car leased for 50000 miles over a period of 3 years? d. What price per mile must be charged in order to earn a profit of $5000 per car over its 3 years life time if it is leased for a total of 50000 miles?
Answers
Answer:
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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