Ware houzer owns a renewable forest land for growing pine trees. Trees can fall into one of four categories depending on their age: baby (0-5 years), young (5-10 years), mature (11-15 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 composition of the forest.

(c) If a new tree is planted at the cost of $1 per tree and a harvester tree has a market value of $20, determine the average annual income from the forest operation.