Gce Model Questions Vol1 2017 Agricultural Science Question 9

A mixed forest stand of species X has an initial basal area of 24 m² ha⁻¹ at age 20 years. Its basal‑area growth follows the logistic equation \(\dfrac{d\text{BA}}{dt}=r\,\text{BA}\bigl(1-\dfrac{\text{BA}}{K}\bigr)\) with \(r=0.04\,\text{yr}^{-1}\) and carrying capacity \(K=48\,\text{m}^2\,\text{ha}^{-1}\). Natural mortality removes 0.5 % of the basal area each year. The manager wishes to keep the basal area constant at its present level (24 m² ha⁻¹) by harvesting the amount of basal area that exactly offsets net growth and mortality. Merchantable timber volume \(V\) (m³ ha⁻¹) is related to basal area by \(V = 0.5\,\text{BA}^{1.5}\). What is the maximum sustainable timber volume that can be harvested each year (in m³ ha⁻¹, to one decimal place)?