IMC is analyzing the cost of having fire extinguishers in optimal condition. Currently there are new fire extinguishers (year 0) which were paid for by the previous administration, which last 8 years, so for this 8th year, new fire extinguishers must also be left for the next administration. In addition, Civil Protection indicates that an extinguisher has a useful life of maximum 3 years if it is maintained every year. A new extinguisher costs $ 2,000, and a used extinguisher can be sold to recoup some of the investment. The costs for the annual maintenance and the sale value of the extinguisher depend on the age of the extinguisher and are indicated in the following table(Please use the method of tables from last to first):

1 2 3 Age of estinguisher Annual maintenance cost Salvage value 300 500 700 1,500 1,400 1,200 Using dynamic programming determines the planning for the purchase, sale and maintenance of the extinguishers that allow to minimize the total cost during the 8 years. Clearly define the decision periods, decision variables, state variables and the solution obtained