Linear Programming Assignment help
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Overview of linear programming
Linear programming is an optimization technique mainly used on problems that can be represented as linear functions. Through linear programming algorithms, an individual is able to determine the optimum point where the function has the highest or the lowest values.
Linear programming is mainly applied in the fields of mathematics, economics, business, and engineering. In the industry, linear programming techniques have been used to solve problems in transportation, telecommunications, energy, and manufacturing.
Basic terminology used in linear programming
- Optimization – It is the selection of the best element from a given set of alternatives.
- Linear equality and inequality – A linear equality is basically a linear equation where a polynomial is equated to zero while a linear inequality is a linear function which involves an inequality sign.
- Constraints – It is a condition of an optimization problem that the solution must meet.
- Feasible region – It is a region with a set of points that satisfy all the constraints of an optimization problem.
- Slack variable – This is a variable that is introduced to a linear inequality to make it linear equality.
Sub-topics covered by our linear programming assignment help service
In linear programming, students are mainly challenged by the various algorithms which are used to carry out optimization. Below are the subtopics under linear programming on which we offer help; including the various methods of solving a linear programming problem.
- Simplex algorithm
The simplex method operates on linear programs in a canonical form. It creates a feasible region at the vertex of the polytope and then follows along the path on the edges of the polytope to the vertices with constant or increasing values of the objective function until an optimum is reached.
In practical situations, the simplex method stands out as the most efficient way of solving linear programming problems.
Other methods which are closely related to the simplex method covered by us are:
- Criss-cross algorithm
- Big M method
- Bland’s rule
- The Klee-Minty cube
- Interior point method
Unlike the simplex method which runs through the edges, the interior point method, just as its name suggests, traverses through the interior of the feasible region to obtain an optimal solution. Methods closely related to the interior point algorithm are:
- Ellipsoid method
- Karmarkar’s method
- Mehrotra predictor-corrector method
- Path following algorithm
- Affine scaling
- Vaidya’s algorithm
- Column generation
Designed for solving large linear programming problems. It is based on the idea that some variables in large linear programs will assume the value of zero. It, therefore, works towards generating only those variables that have the potential to improve the objective function.
- k-approximation of k-hitting set problems
- Vertex enumeration problems
- LP-type problems
- Fourier-Motzkin elimination problems
- Hilbert basis linear programming
- Linear inequalities
- Basic solution linear programming
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