Neco 2024 Agricultural Science Question 33

A mixed teak plantation is established on 100 ha. After clear‑felling, a regeneration period of 5 years yields an initial stand volume of 10 m³ ha⁻¹. Thereafter the stand follows the logistic growth model\n\[\nV(t)=\frac{K}{1+A e^{-r t}},\n\]\nwhere \(K=200\;\text{m}^3\text{ha}^{-1}\), \(r=0.08\;\text{yr}^{-1}\) and \(A=\frac{K-V_0}{V_0}=19\). The stand is harvested at age \(5+t\) years, giving a harvest volume \(V(t)\). The farmer wishes to adopt a rotation system that provides a continuous annual supply of timber by rotating equal‑size plots. Determine the rotation length (in years, including the 5‑year regeneration period) that maximises the average annual timber yield per hectare, and compute that maximum average yield (in m³ ha⁻¹ yr⁻¹, to two decimal places).