We assume that the permissible harvest age for both pure poplar forest and agro-forestry ranges
from n to m. That is, the poplar cannot be harvested before age n and it must be harvested once it
reaches age m. The starting year of planting button mushroom under poplar is f (f < n) due to shade
environment it needs to grow. And the relationship between poplar and button mushroom is that
when button mushroom planting is stopped, the forest could be kept for further growth, but when
poplar is harvested button mushroom planting must be stopped. The second assumption is that the
button mushroom price is constant during each growing season, which is about 4 months; but due to
the long production period of forest, we take the uncertainty of timber price into consideration. The
timber prices at time t is modeled as: