Solve using Excel

Warehouzer owns a renewable forest land for growing pine trees. Trees can fall into one of four categories depending on their age: baby (0 to 5 years), young (5 to 10 years), mature (11 to 15 years), and old (more than 15 years). Ten percent of baby and young trees die before reaching the next age group. For mature and old trees, 50% are harvested and only 5% die. Because of the renewal nature of the operation, all harvested and dead trees are replaced with new (baby) trees by the end of the next 5-year cycle. (a) Express the forest dynamics as a Markov chain. (b) If the forest land can hold a total of 500,000 trees, determine the long-run com- position of the forest. (c) If a new tree is planted at the cost of $1 per tree and a harvested tree has a market value of $20, determine the average annual income from the forest operation. Warehouzer owns a renewable forest land for growing pine trees. Trees can fall into one of four categories depending on their age: baby (0 to 5 years), young (5 to 10 years), mature (11 to 15 years), and old (more than 15 years). Ten percent of baby and young trees die before reaching the next age group. For mature and old trees, 50% are harvested and only 5% die. Because of the renewal nature of the operation, all harvested and dead trees are replaced with new (baby) trees by the end of the next 5-year cycle. (a) Express the forest dynamics as a Markov chain. (b) If the forest land can hold a total of 500,000 trees, determine the long-run com- position of the forest. (c) If a new tree is planted at the cost of $1 per tree and a harvested tree has a market value of $20, determine the average annual income from the forest operation