Neco Model Questions Vol1 2021 Agricultural Science Question 5

A 200‑ha forest is to be managed for timber and carbon credits. Two species are available:\n\n- Species C: initial stock 50 m³ ha\(^{-1}\), annual growth 4 % (compounded), harvested after 20 years. 30 % of the harvested volume remains as residues for carbon credits.\n- Species D: initial stock 30 m³ ha\(^{-1}\), annual growth 6 % (compounded), harvested after 12 years. 20 % of the harvested volume remains as residues for carbon credits.\n\nTimber prices are $150 m\(^{-3}\) for species C and $180 m\(^{-3}\) for species D. Carbon credits are $12 per tonne of carbon, and 1 m³ of wood contains 0.5 tonne of carbon (so $6 per m³ of wood). The processing plant can handle at most 5 000 m³ of timber per year. Biodiversity regulations require that at least 30 % of the forest area be planted with species C.\n\nAssuming the manager can allocate any proportion of the 200 ha to each species and that each species is replanted immediately after harvest, determine the optimal allocation (percentage of area to species C and to species D) that maximises the total annual net revenue (timber plus carbon credits) over a 24‑year horizon, while respecting the processing capacity and biodiversity constraint. State the optimal percentages (to the nearest whole percent) and the corresponding maximum annual net revenue (in $).