  We consider semi-linear elliptic equations of the following form:
\begin{equation*} \left\{ \begin{aligned}
  -\Delta u &= \lambda[u-\dfrac{u^2}{K}-c \dfrac{u^2}{1+u^2}-h(x) u]=:\lambda
f_h(u), \quad && x \in \Omega,
  \frac{\partial u}{\partial \eta}&+qu = 0, \quad && x\in\partial\Omega,
\end{aligned} \right. \end{equation*}
  where, $h\in U=\{h\in L^2(\Omega): 0\leq h(x)\leq H\}.$ We prove the
existence and uniqueness of the positive solution for large $\lambda.$ Further,
we establish the existence of an optimal control $h\in U$ that maximizes the
functional $J(h)=\int_{\Omega}h(x)u_h(x)~\rm{d}x-\int_{\Omega}(B_1+B_2
h(x))h(x)~\rm{d}x$ over $U$, where $u_h$ is the unique positive solution of the
above problem associated with $h$, $B_1>0$ is the cost per unit effort when the
level of effort is low and $B_2>0$ represents the rate at which the cost rises
as more labor is employed. Finally, we provide a unique optimality system.
