Question

Cheapest Car Rental rents cars at the Chicago airport. The car rental market consists of two segments: the short-term segment, which rents for an average of 0.8 weeks, and the medium-term segment, which rents for an average of 2 weeks. Cheapest currently rents an average of 200 cars a week to the short-term segment and 100 cars a week to the medium-term segment. Approximately 20 percent of the cars returned (evenly distributed across both segments) are found to be defective and in need of repairs before they can be made available for rent again. The remaining cars, not needing repairs are cleaned, filled with gas, and made available for rent. On average, there are 92 cars waiting to be cleaned (or in the cleaning process). The average cost of this operation is $5 per car. Cars needing repair spend an average of two weeks out of service and incur an average cost of $150 per car. Assume that cars are rented as soon as they are available for rent, that is, as soon as they have been cleaned or repaired. Short term renters pay $200 per week (not $200 per rental - rental time is shorter than a week), while medium term renters pay $120 per week. Assume each car loses $40 in value per week due to depreciation. What is the average weekly profit rounded to the nearest whole dollar?

Answer 1

Firstly, we will calculate the total income

Income from short term segment cars in a week = 200 × $200 = $40000

Income from middle term segment cars in a week = 100 × $120 = $12000

Total income = $40000 + $12000 = $52000

Now, we will calculate the expenses

20% cars returned are found to be defective and evenly distributed between both segments, i.e. , 10% of cars from short term segment and 10% cars from middle term segment.

= 10% of 200 cars + 10% of 100 cars

= 20 + 10 cars

= 30 cars

Reparing cost per car = $150

Reparing cost of 30 cars = $150 × 30

= $4500

Now, cleaning cost per car = $5

Cleaning cost for 92 cars = $5 × 92

= $460

Depreciation cost per car = $40

As their are total of 300 cars ( 200 in short term + 100 in long term)

Total cost of depreciation of 300 cars = $40 × 300

= $12000

Total expences = $4500 + $460 + $12000

= $16960

Total average profit in a week = $52000 - $16960

= $35040