Linear programming currently occupies a prominent position in various fields and has wide applications, as its importance lies in being a means of studying the behavior of a large number of systems as well. It is also the simplest and easiest type of model that can be created to address industrial, commercial, military and other dilemmas. Through which to obtain the optimal quantitative value. In this research, we deal with the post optimality solution, or what is known as sensitivity analysis using the principle of shadow prices. The scientific solution to any problem is not a complete solution once the optimal solution is reached. Any change in the values of the model constants or what is known as the inputs of the model will change the problem of linear programming and will affect the optimal solution. Therefore, we need a method that helps to stand on the impact of changing these constants on the optimal solution that has been reached. General concepts about the binary model and some related theories have also been addressed. By analyzing the sensitivity, we rely on real data for a company that transports crude oil and its derivatives. The mathematical model is formulated for it and the optimal solution is reached using the software. Ready-made sop WINQSB and then calculate the shadow price values for the binding constraints, in addition, linear programming under the fuzzy environment is reviewed, and a new method based on the prime numbers is used to solve the fuzzy parameters model.