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I am having problems with this home work. I understand it is a shortest path problem. I can't seem to set it up correctly.

I am having problems with this home work. I understand it is a shortest path problem. I can't seem to set it up correctly. The problem reads

At the beginning of year 1, a new machine must be purchased. The cost of maintaining a machine i years old and the cost of purchasing a machine at the beginning of each year are given in the tables below. 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.

Age at the        Maintenance Cost

Beg of Yr          for Next Yr ($)

0 38,000

1 50,000

2 97,000

3 182,000

4 304,000


Year   Purchase Cost

1  170,000

2 190,000

3 210,000

4 250,000

5 300,000


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