In this research , the formulation of optimum cost design for one way reinforced concrete slabs is presented , since it is useful and have a widespread usage among practicing engineering and applied to realistic structures subjected to the actual constraints of commonly used design codes such as the American concrete instituted code (ACI,2005).

The formulation contains minimizing an objective function that represent the cost of steel reinforcement and the cost of concrete , which is subjected to many constraints containing : flexural constraints , serviceability constraints and deflection constraints that illustrated with details in this paper . the optimum solution is calculated using the lagrangian multipliers method , and a visual basic computer software were developed to find the optimum solution .

Key Words: Optimization , Lagrangian Multiplayer , Optimum Cost Design . One way Slabs .