The work being presented in this thesis is devoted to investigate the different techniques for solving Quadratic Programming Problems (QPP) and Non-Linear Programming Problems (NLPP). We first develop a technique to generalize the traditional simplex method for solving a special type (Quasi-concave) QPP in which the objective function can be factorized. We then investigate three well known methods in Operation Research known as Lagrange''s method, Karush-Kuhn-Tucker (KKT) method and Wolf''s method for solving QP and NLP problems. Graphical representation of the above three methods are also demonstrated along with their merits and demerits. We implement Lagrange''s method for solving any type of NLPP. For this, we develop a computer technique along with algorithm. We then develop another computer technique for the implementation of KKT method for solving any NLPP. We also modify Wolf''s method to solve any type of QP problems. For this, we develop a computer technique. All the codes in this thesis are developed by using the programming language Mathematica. To demonstrate all of our computer codes, we illustrate number of numerical examples.