Park owns a cafe. He heard that handmade ice cream is getting popular. So, he is trying to sell handmade ice cream in his cafe. For this, he plans to buy an ice cream machine, and how long to use that machine. At the beginning of year 1, a new ice cream machine must be purchased.

Table 1 shows the cost of maintaining a machine i years old. As the machine gets old, its maintenance cost increases rapidly. The cost of purchasing a machine at the beginning of each year is given in Table 2. More and more cafes are trying to sell ice cream, and the price of the machine will increase every year. There is no trade-in value when a machine is replaced. Your goal is to minimize the total cost (purchase plus maintenance) of having a machine for five years. Determine the years in which a new machine should be purchased.

Find out the cost minimized plan.

Age at beginning of year 0 1 2 3 4 Maintenance cost for next year($) 38000 50000 97000 182000 304000 Table 1 Year Purchase Cost($) 170000 1 2 190000 3 210000 4 250000 5 300000 Table 2 Age at beginning of year 0 1 2 3 4 Maintenance cost for next year($) 38000 50000 97000 182000 304000 Table 1 Year Purchase Cost($) 170000 1 2 190000 3 210000 4 250000 5 300000 Table 2