## (solution) (20 points) A new police car costs the Bay City Police Department

(20 points) A new police car costs the Bay City Police Department \$25,000. The annual maintenance

cost for a car depends on the age of the car at the beginning of the year. (All cars accumulate

approximately the same mileage each year.) The maintenance costs increase as a car ages, as shown

in the following table:

Period Annual Maintenance Cost

1st year 1000

2nd year 4000

3rd year 6000

4th year 8000

5th year 10000

Note that a car cannot be used after 5 years, it should be discarded after 5 years. In order to avoid the

increasingly high maintenance costs, the police department can sell a car and purchase a new car at the

end of any year. The selling price for a car at the end of each year of use is also shown in the table.

At the end of year Used Selling Price

1 15000

2 13000

3 10000

4 7000

5 2000

It is assumed that the price of a new car will increase \$500 each year. The department?s objective is to

develop a car replacement schedule that will minimize total cost (i.e., the purchase cost of a new car

plus maintenance costs minus the money received for selling a used car) during the next 6 years (until

the end of year 6). Develop a car replacement schedule, using the shortest route method

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Sep 13, 2020

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