The untreated grey water generated by domestic activities is the major sanitation problem. From the industrial point of view, the modeling approach of three parameter isotherm model Redilch-Peterson based on the column system has been considered. A theoretical one dimension dynamic model was proposed to understand the behaviour in fixed bed, assuming Straight run mode to study the phenomenon of adsorption. Using MATLAB linear programming and least square method the parameters involved have been optimized. Thus predicted results are correlated with the theory and experimental observation available in the literature using Mathematical derivation and MATLAB. Thus a modified Redilch-Peterson isotherm model in packed bed for waste water treatment has been proposed.