Car rental services normally offer two rates.

• Standard daily rate plus cents per mile
• Unlimited mileage per day

Which rental plan you should choose depends on how far you will go during the trip. The math concept that will help you make the choice is called the breakeven analysis. Below is a table for the rental cost.

 Model Standard Daily Rate (Dollars) Plus Cents Per Mile Unlimited Mileage Daily (Dollars) Sub-Compact 40 15 70 Compact 45 21 75 Midsize 49 23 80 Station Wagon 55 25 89 Van 64 28 100 Luxury 70 30 105

For standard daily rate plus cents per mile rental plan:

TC = FC + VC

where

TC = Total Cost (Total rental cost per day)

FC = Fixed Cost (Standard daily rate)

VC = Variable Cost (cents per mile ´ number of miles driven)

or

For unlimited mileage plan:

TC = UMD

where

UMD = Unlimited Mileage Daily

Rose and her family are going to Sacramento for a one day trip. They plan to rent a station wagon. What is the breakeven point of the rental costs? (The total number of miles that they drive makes the cost the same for limited and unlimited mileage)

m = total number of miles driven

Total Cost (Limited)  = Total Cost (Unlimited )

55 + (0.25 ´ m) = 89

0.25 ´ m = 34

m = 136

At 136 miles, the cost for the unlimited mileage and the limited mileage is equal. If you travel more than 136 miles, take the unlimited, but if you travel less than that, take the limited.

Michelle and her family are going on a vacation trip to Salt Lake City, Utah, from their home town, Rancho Palos Verdes. The total driving distance is 1,700 miles and the trip will last one week (7 days). If they are renting a midsize car which rental option should they take?

Unlimited mileage

Limited mileage