Question

2. automobile leasing: 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 $4500. the owner of the agency estimates that variable cost of operating the cars, exclusive of the 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 a total cost function associated with renting a car for total of x miles over 3 year period c. formulate a profit function d. what is the profit if 10000 units are produced and sold during the year? e. what level of output is required in order to earn zero profit?

Answer 1

(a)new car cost = $ 15,00

selling price = $ 3,600

total fixed cost involved = 15000 - 3600

= $ 11,400

variable cost per miles =$ 0.16

revenue per mile = $ 0.33

contribution per mile = revenue per mile - variable cost per miles

= 0.33 - 0.16

=$ 0.17

$\text{break\: even\: mileage} = \dfrac{\text{ fixed \: cost }}{\text{contribution \: per \: unit} }$

$\text{ break\: even\: mileage } = \dfrac{11400 }{0.17 }$ =67058.82

(b) total number of miles = 50,000

total profit = contribution per miles x total miles - fixed cost

= 0.17 x 50,000 - 11400

= $ 8500 - 11400

= - $ 3100 (loss)

total cost = fixed cost + variable cost x total miles

= 11400 + 0.16 x 50,000

= 11400 + 8000

= $ 19400

total revenue = revenue per unit x total miles

= 0.33 x 50000

= $ 16500

(c)

if break even miles = 50,000

$\text{ break\: even\: mileage }= \dfrac{\text{ fixed \: cost } }{\text{contribution \: per \: unit} }$

$50,000 = \dfrac{11400 }{\text{contribution \: per \: mile }}$

$\text{ contribution \: per \: mile }= \dfrac{11400 }{50,000 }$

contribution per miles = 0.228

(d)

profit = 5000

total revenue = profit + TC

= 5000 + 19400

= 24,400

$\text{revenue per unit} = \dfrac{\text{total revenue} }{ \text{total miles}}=\dfrac{24400}{50000}=0.488$

(e) Level of output to earn zero profit-

total profit = contribution per miles x total miles - fixed cost

$\Rightarrow 0= x\times 50,000 - 11400 \\ \Rightarrow x=\dfrac{11400}{50000}=0.228$