Pacific Pulp and Paper is deciding how to manage their main forest. They have trees at a variety of ages, which we will break into Classes 1 to 4 . Currently, they have 8000 acres in Class 1 , 10,000...

Pacific Pulp and Paper is deciding how to manage their main forest. They have trees at a variety of ages, which we will break into Classes 1 to 4 . Currently, they have 8000 acres in Class 1 , 10,000 acres in Class 2 , 20,000 in Class 3, and 60,000 in Class 4 . Each class corresponds to about 25 years of growth. The company would like to determine how to harvest in each of the next four 25- year periods to maximize expected revenue from the forest. They also foresee the company’s continuing after a century, so they place a constraint of having 40,000 acres in Class 4 at the end of the planning horizon. Each class of timber has a different yield. Class 1 has no yield, Class 2 yields 250 cubic feet per acre, Class 3 yields 510 cubic feet per acre, and Class 4 yields 700 cubic feet per acre. Without fires, the number of acres in Class i (for i = 2,3 ) in one period is equal to the amount in Class i−1 from the previous period minus the amount harvested from Class i − 1 in the previous period. Class 1 at period t consists of the total amount harvested in the previous period t −1 , while Class 4 includes all remaining Class 4 land plus the increment from Class 3. While weather effects do not vary greatly over 25-year periods, fire damage can be quite variable. Assume that in each 25-year block, the probability is 1/3 that 15% of all timber stands are destroyed and that the probability is 2/3 that 5% is lost. Suppose that discount rates are completely overcome by increasing timber value so that all harvests in the 100-year period have the same current value. Revenue is then proportional to the total wood yield.