The exhaustive list of topics in Linear programming in which we provide Help with Homework Assignment and Help with Project is as follows:

- Linear models such as; Product mix problem, Nutrition Problem,a BlendingProblem, Formulation of these problems as Linear Programming problems (LLP). Axioms of linearity, General form of LPP, Slack and Surplus Variables. Standard Form of LPP.
- Basic concepts of rank of a matrix, Solution of a system of linear equations, Examples. Basic feasible solution (bf s), degenerate and non-degenrate, examples of basic solutions which are not feasible. Upper bound on the number of bf s. Upper bound on the absolute value of the basic variables.
- Existence of bf s, Moving from one bfs to another and improving the value of the objective function. Optimality Criteria. Optimal solution is a bfs. Simplex algorithm through a simple example.
- Simplex algorithm - geometrically interpretation. Definition of an affine space, Polyhedron P, faces of a polyhedron – facets, edges and vertices. Representation of a polyhedron in terms of extreme points and extreme rays.
- A basic feasible solution is an extreme point of the corresponding Polyhedron. More about degeneracy.
- Supporting hyperplane of a polyhedron. Characterisation of an optimal solution in terms of supporting hyperplane. Graphical illustrations.
- Simplex Algorithm- Tableau format.
- Simplex algorithm – Starting feasible solution, Artificial variables, Phase I and Phase II methods.
- Bounded variables case; modification of the Simplex algorithm.
- Revised Simplex algorithm. Define the Dual problem and its various forms. Fundamental Theorem of Duality. Farka’s theorem. Complementary Slackness theorem.
- Dual Simplex algorithm; Motivation , theory and a numerical example.
- Primal Dual algorithm: Motivation , theory and a numerical example.
- Sensitivity Analysis of the objective function coefficient, right hand side components and elements of the matrix A.
- Adding of constraints and activities. A comprehensive numerical example.
- Parametric analysis.
- Min-cost flow problem- formulation and derivation of special cases such as Transportation problem.
- Assignment problem, Max-flow problem and the shortest path problem.
- Integer bfs property of Transportation problem.
- Simplified Simplex algorithm for Transportation problem.
- Sensitivity Analysis and Bounded Variable case.
- Formulation of Shortest Path Problem, Dijkstra’s algorithm.
- More general shortest Path algorithms, Sensitivity analysis.
- Applications of Max-flow problem.
- Algorithms and Sensitivity Analysis.
- Network Simplex Algorithm for Min – cost flow problem.
- Project Planning Control with PERT / CPM, linear programming formulations.
- Dynamic Programming: Principle of Optimality with proof. Discrete and continuous problems.
- Backward and forward formulations. Probabilistic cases.
- Game theory. Two-person Zero-sum game. Pure and mixed strategies with examples.
- Saddlepoint and graphical solutions.
- Linear programming iterative solution method.
- Computational complexity of Simplex algorithm. To show through an example that the Simplex algorithm can go through all the extreme points before reaching the optimal extreme point solution.
- Ellipsoid algorithm- basic concepts and its applications.
- Basic idea behind Karmarkar’s algorithm and its applications.