The Pine Christmas Tree Farm owns a plot of land with 5000 evergreen trees. Each year, the owner allows retailers of Christmas trees to select and cut trees for sale to individual customers. The farm protects small trees (usually less than 4 feet tall) so that they will be available for sale in future years. Currently, 1500 trees are classified as protected trees, while the remaining 3500 are available for cutting. However, even though a tree is available for cutting in a given year, it may not be selected for cutting until future years. Most trees not cut in a given year live until the next year, but some diseased trees are lost every year. In viewing the Christmas tree operation as a Markov process with yearly periods, we define the following four states: (1) Cut and sold, (2) Lost to disease, (3) Too small for cutting, (4) Available for cutting but not cut and sold. The following transition matrix is appropriate: States (1) (2) (3) (4) (1) 1 0 0 0 (2) 0 1 0 0 (3) 0.1 0.15 0.5 0.25 (4) 0.3 0.1 0 0.6 How many of the farm’s 5000 trees will be sold eventually, and how many will be lost?
The Pine Christmas Tree Farm owns a plot of land with 5000 evergreen trees. Each year, the owner allows retailers of Christmas trees to select and cut trees for sale to individual customers. The farm protects small trees (usually less than 4 feet tall) so that they will be available for sale in future years. Currently, 1500 trees are classified as protected trees, while the remaining 3500 are available for cutting. However, even though a tree is available for cutting in a given year, it may not be selected for cutting until future years. Most trees not cut in a given year live until the next year, but some diseased trees are lost every year. In viewing the Christmas tree operation as a Markov process with yearly periods, we define the following four states: (1) Cut and sold, (2) Lost to disease, (3) Too small for cutting, (4) Available for cutting but not cut and sold.
The following transition matrix is appropriate:
| States | (1) | (2) | (3) | (4) |
| (1) | 1 | 0 | 0 | 0 |
| (2) | 0 | 1 | 0 | 0 |
| (3) | 0.1 | 0.15 | 0.5 | 0.25 |
| (4) | 0.3 | 0.1 | 0 | 0.6 |
How many of the farm’s 5000 trees will be sold eventually, and how many will be lost?
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