Mr Chan lives in Tai Po and he determines to ride a bicycle from home to the railway station rather than catching the bus daily. Now, he wants to determine the cheapest way to keep a bicycle over the 5-year timeframe. A new bicycle costs $1000 and the maintenance costs vary with the age of the bicycle: $100 (in the first year), $200 (in the second year) and $400 (in the third year). Assuming that the bicycle can last for 3 years before it is sold and he figures out that he can get $400 if he sells the bicycle after one year of use, $300 after two years of use and 200 after three years of use. When should he buy bicycles and how long should he keep them to minimize the total costs over the entire 5-year period?

The answer: min. cost $ 2500 by keep a bike for 2 years and then another one for the following 3 years.

Requires for step by step answer.