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Linear Programming - Essay Example

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Introduction Linear programming is a mathematical process of optimization by which one minimizes or maximizes a given function known as the objective function, subject to a finite number of linear constraints, which may be in the form of equations or inequalities (Karloff, 2008)…
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Linear Programming essay
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Linear Programming

The applications of linear programming span providing solutions to problems involving economics, computer science, and practically any other industry that requires a production schedule or an actual scheduling process. Moreover, the optimizing feature of linear programming makes it a necessity for people in the management circle to be familiar with. Simplex algorithm A linear programming model is typically solved using a simplex algorithm, or sometimes also referred to as the linear solver (Powell & Baker, 2010). The simplex algorithm involves a series of steps which employs the use of slack and basic variables to change the inequality constraints to equations so that the derived system of equations may be solved to find a feasible solution area. The extreme points of this feasible solution area are then tested by plugging them in to the objective function in order to find out which gives the optimal solution (Singiresu, 2009). Linear Programming Models There are a number of models that may be used to generate the solution to a linear programming model. ...
Such models are generally used in manufacturing companies or supply chain networks. Another kind of linear programming model involves the blending of a number of resources to produce desired results, hence the term blending model (Baker, 2011). A typical example of this model is the “diet problem” wherein one aims to find the optimum mix of food products that will produce the maximum nutritional value. The covering model of linear programming is quite different from the first two models in such that it aims to minimize the objective function and is presented with “greater than constraints” (Powell & Baker, 2010, p. 79). This model is commonly used when minimizing a cost function and requiring the contributions to be greater than a particular value. Finally, the network model is quite unique in nature as it “describes configurations of flow in a connected system” (Baker, 2011, p. 71). Typically, a network model would require the use of a diagram which aids in the finding of the optimal solution of a given problem. In all these types of linear programming models, spreadsheets may be used to provide assistance in finding the optimal solution. Excel has a built in Solver application which allows the user to simply input the coefficients of the objective function and constraints, and automatically generates values for the feasible region and the corresponding optimal solution. Sensitivity Analysis It should be noted that the task is not yet done when the optimal solution is found. It is also necessary to conduct a corresponding sensitivity analysis on the solution generated. Sensitivity analysis provides information on how instantaneous changes in the parameters of the problem would affect the optimal solution ... Read More
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