A Modified Quick Convergent Inflow Algorithm (MQCIA) for Solving Linear Programming problems, based on variance of predicted response, is presented. The method adds a point of maximum variance to an initial design thus leading to a maximizer of the response function in a maximization problem. Similarly, a point of minimum variance is added to an initial design thus leading to a minimizer of the response function in a minimization problem. Effectiveness of the method has been demonstrated and the results show that by improving an existing experimental design, the optimizer of the response function is approached. Analytical justification for the MQCIA has also been established.