We study positive solutions to the steady state reaction diffusion
equation with Dirichlet boundary condition of the form:
\begin{equation}
\left\{
\begin{aligned}
-\Delta u &= au-bu^2-c \dfrac{u^p}{1+u^p}-K, \quad x \in \Omega
\\u &= 0, \quad x \in\partial\Omega.
\end{aligned} \right.
\end{equation}
Here $\Delta u=div \big(\nabla u\big)$ is the Laplacian of u, $a, b,
c, p, K$ are positive constants with $p\geq2$ and $\Omega$ is a
smooth bounded region with $\partial\Omega$ in $C^2$. This model
describes the steady states of a logistic growth model with grazing
and constant yield harvesting. It also describes the dynamics of the
fish population with natural predation and constant yield
harvesting. We study the existence of positive solutions to this
model. We prove our results by the method of sub-super solutions.