Answer to Question #188315 in Statistics and Probability for Hizwa Zeeshan

Question #188315

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?


1
Expert's answer
2021-05-07T10:29:49-0400

(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\n\\\\\n \\Rightarrow x=\\dfrac{11400}{50000}=0.228"



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