Models & Qualitative Behavior · Challenge problem

A fishery with logistic growth $P' = 0.6P\left(1 - \dfrac{P}{2000}\right)$ is fished with constant effort $E$, removing $EP$ fish per year, so $P' = 0.6P\left(1 - \dfrac{P}{2000}\right) - EP$. The stock settles at its positive stable equilibrium and the yearly catch there is $EP^*$. Which effort $E$ maximises this sustained catch?