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This book for engineering students studying in B.Tech., III semester (CS and IT Branch) of Rajasthan Technical University and all Indian Universities. Each chapter begins with a clear statement of pertinent definitions, together with illustrative. A large number of supplementary problems with answers serve as a complete review of the material of each chapter. However, the book can be used as an advantage by B.Tech and post graduate students of various universities who have no prior experience with Optimization Techniques such as linear programming problems, project scheduling, CPM, PERT, sequencing problems, laplace transform and numerical methods. This book has been divided into five units. Unit I deals with introduction to optimization, statement, application of optimization techniques and classical optimization techniques. Unit II describes the introduction of linear programming problem, formulation of linear programming problem, solution of linear programming problem by graphical method, simplex method, duality in linear programming problem and transportation problem. Unit III provides a detailed coverage of project scheduling, CPM, PERT and sequencing problems of n-jobs with two machines, n-jobs with k-machines and two jobs with k-machines. Unit IV contains an introduction to laplace transform with its simple properties, inverse laplace transform, convolution theorem, heaviside expansion formula and application of laplace transform to solution of ordinary and partially differential equation with constant coefficient. Unit V focuses on numerical methods, finite differences, Newton’s forward and backward differences formula, Stirling’s formula, Lagrange’s interpolation, inverse interpolation formula, numerical differentiation and integration, and numerical solution of differential equation of first order. Table of Contents UNIT-I: Introduction—Introduction to Optimization Classificial Optimization Techniques UNIT-II: Linear Programming—Linear Programming Problem and Graphical Method The Simplex Method Duality in Linear Programming Transportation Problem UNIT-III: Project Scheduling—Networking with CPM & PERT Sequencing UNIT-IV: Laplace Transform—Laplace Transform The Inverse Laplace Transform Applications of Laplace Transform to Solve Differential Equation UNIT-V: Numerical Methods—Calculus of Finite Differences Interpolation Numerical Differentiation Numerical Integration Ordinary Differential Equations of First Order Difference Equation Paper.