In the Simplex Method, the cost of beam is the objective function, while the constraints are computed in accordance with the design critia of partially prestressed concrete beams. Variables in the objective function and the constraints are the area of prestressed reinforcement, the area of nonprestressed reinforcement, the distance from extreme compression fiber to centroid of prestressing steel and the stimup spacing. The objective function and constraints thus obtained will consist of non-linear terms The linearization of above equations is done by using the first and second terms of Taylor series. In the linear programming solver process, the computation will repeat until the solution satisfies all onginal constraints and the difference of the two consecutive values of the cost is less than 0.05%,