Formulation of linear programming models: objective function, constraints, standard maximization and minimization problems. Feasibility, unboundness, multiple optimal solutions. Solution with graphical representation. Simplex algorithm and method: slack variables, optimality conditions, artificial variables. Simplex algorithm in matrix form. The two-phase simplex method. The big-M method. Duality, the Duality Theorem, financial interpretation of the Dual. The Dual simplex method. Sensitivity Analysis, changes on the values of the objective function and the Right Hand Side values. Integer linear programming, production planning, transportation problems.
