Neco Model Questions Vol1 2022 Agricultural Science Question 30

A forest of 200 ha is planted with a fast‑growing species whose mean merchantable volume (in m³ ha\(^{-1}\)) follows the logistic model\n\[\nV(t)=\frac{200}{1+e^{-0.2\,(t-10)}}\n\]\nwhere \(t\) is the age in years. The forest is managed under a rotation system: each year a proportion \(p\) of the total area is harvested when the trees reach age \(L\) years, and the harvested area is immediately replanted. Consequently \(p=\frac{1}{L}\). The rotation period must be at least 10 years. (a) Express the average annual sustainable yield (in m³ yr\(^{-1}\)) as a function of \(L\). (b) Determine the value of \(p\) that maximizes this average yield and give the corresponding maximum sustainable yield, rounded to the nearest whole number.