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We study the positive solutions to steady state reaction diffusion equations with Dirichlet boundary conditions of the forms: \begin{align} -u''&=\left\{\begin{array}{ll} \lambda[au-bu^{2}-c], & x\in(L,1-L),\\ \lambda[au-bu^{2}], & x\in(0,L)\cup(1-L,1), \end{array} \right.\tag{A}\\ u(0)&=0 =u(1),\nonumber \end{align} and \begin{align} -u''&=\left\{\begin{array}{ll} \lambda[au-bu^{2}-c], & x\in(0,\frac{1}{2}),\\ \lambda[au-bu^{2}], & x\in(\frac{1}{2},1), \end{array} \right.\tag{B}\\ u(0)&=0 =u(1).\nonumber \end{align} Here $\lambda, a, b, c$ and $L$ are positive constants with $0<L<\frac{1}{2}$. Such steady state equations arise in population dynamics with logistic type growth and constant yield harvesting. Here $u$ is the population density, $\frac{1}{\lambda}$ is the diffusion coefficient and $c$ is the harvesting effort. In particular, model A corresponds to a symmetric harvesting case and model B to an asymmetric harvesting case. Our objective is to study the existence of positive solutions and also discuss the effects of harvesting. We will develop appropriate quadrature methods via which we will establish our results.