Background and Objectives: Linear Programming (LP) is an easy way to optimize diet cost in which nutritional requirements are also met. Although LP was used for children, it has not been run to design a diet for patients with renal diseases. The aim of this study was to design a cost-optimized meal by LP for patients with kidney disease in which essential nutritional requirements are met.Materials and Methods: For this cross-sectional study, two combinatorial meals were considered, and their ingredients were chosen from the restaurant recipes. Minimum and maximum amounts for each ingredient were determined. The price of ingredients was gathered from authentic stores selling foods with approved price. The requirements for energy, protein, sodium, potassium and phosphorus expected to meet by this meal were also determined. The LP was run by Microsoft Excel. Optimized cost was calculated in while essential nutritional requirements were also met.Results: The amounts determined by LP were between the min and max, and all needs were met by the designed meals. Diet cost was also optimized.Conclusion: LP could be used to design low-cost meals for patients with kidney disease.

In this study, we discussed a fuzzy Programming approach to bi-level Linear Programming problems and their application. Bi-level Linear Programming is characterized as mathematical Programming to solve decentralized problems with two decision-makers in the hierarchal organization. They become more important for the contemporary decentralized organization where each unit seeks to optimize its own objective. In addition to this, we have considered Bi-Level Linear Programming (BLPP) and applied the Fuzzy Mathematical Programming (FMP) approach to get the solution of the system. We have suggested the FMP method for the minimization of the objectives in terms of the Linear membership functions. FMP is a supervised search procedure (supervised by the upper Decision Maker (DM)). The upper-level decision-maker provides the preferred values of decision variables under his control (to enable the lower level DM to search for his optimum in a wider feasible space) and the bounds of his objective function (to direct the lower level DM to search for his solutions in the right direction).

In this paper, a new method is proposed to find the fuzzy optimal solution of fully fuzzy Linear Programming (abbreviated to FFLP) problems. Also, we employ Linear Programming (LP) with equality constraints to find a non-negative fuzzy number vector x˜ whic h satisfies A˜x˜=b˜, where A˜ is a fuzzy number matrix. Then we investigate the existence of a positive solution of fully fuzzy Linear system (FFLS).