This article offers a comparative study of maximizing and modelling production costs by means of composite triangular fuzzy and trapezoidal FLPP. It also outlines five different scenarios of instability and has developed realistic models to minimize production costs. Herein, the first attempt is made to examine the credibility of optimized cost via two different composite FLP models, and the results were compared with its extension, i.e., the trapezoidal FLP model. To validate the models with real-time phenomena, the Production cost data of Rail Coach Factory (RCF) Kapurthala has been taken. The lower, static, and upper bounds have been computed for each situation, and then systems of optimized FLP are constructed. The credibility of each model of composite-triangular and trapezoidal FLP concerning all situations has been obtained, and using this membership grade, the minimum and the greatest minimum costs have been illustrated. The performance of each composite-triangular FLP model was compared to trapezoidal FLP models, and the intense effects of trapezoidal on composite fuzzy LPP models are investigated.