Question
A used car dealership is trying to keep track of its inventory. A vehicle can be placed in five categories: Sold (S), For Sale -
A used car dealership is trying to keep track of its inventory. A vehicle can be placed in five categories: Sold (S), For Sale - Full Price (F), For Sale - Discounted Price (D), In Repair (R), or Junk (J).
If a car is classified as (S) in one period it will definitely be classified as (S) in the next period. If a car is classified as (F), then in the next period it will be (S) with a probability of 0.25, (F) with a probability of 0.4, (D) with a probability of 0.2, and (R) with a probability of 0.15. If a car is classified as (D), then in the next period it will be (S) with probability 0.4, (D) with probability 0.4, and (R) with probability 0.2. If a car is classified as (R), then in the next period it will be (F) with probability 0.2, (D) with probability 0.3, (R) with probability 0.3, and (J) with probability (0.2). Finally, if a car is (J), then it will remain in this category in the next period.
Currently there are 20 cars for sale at full price, 40 for sale at a discounted price, and 10 in repair. How many cars should we expect to eventually be sold, and how many should we expect to eventually be junk?
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