In this paper the optimal solution for linear programming is derived where some parameters are fuzzy in numbers. In practice, there are many problems arise if the decision parameters are crisp in nature, and such problems are usually solved by introducing either probabilistic programming or multi objective programming methods. Unfortunately all these methods have shortcomings. In this note, the concept of fuzzy numbers is introduced, which is a very effective method for solving these problems. With the problem assumptions, the optimal solution can still be theoretically solved using the simplex based method. Fuzzy decision variables can be initially generated and then solved and improved sequentially using the fuzzy decision approach by introducing robust ranking technique. The proposed procedure was programmed through MATLAB (R2009a) version software for representing four dimensional slice diagrams to its application. The model is illustrated with an application which incorporates all concepts of a fuzzy arithmetic approach to draw managerial insights.