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Linear and Non-Linear Programming - Report Example

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This report "Linear and Non-Linear Programming" focuses on the problem that linear and non-linear programming does have any economic values. Most of the economic decisions can be taken based on linear and non-linear problem-solving methods. …
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Linear and Non-Linear Programming
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Download file to see previous pages Regression, for example, may help the manager to forecast his sales based on past records, but he must make sure that the user of his product has not undergone any changes in taste and preference. Therefore, an econometric model may prove a better aid than pure mathematics and statistics.
In linear programming, the statement of the optimization (maximization or minimization, as the case may be) problem runs in a linear form where these variables are restricted to values satisfying a system of linear constraints, i.e., a system of linear equations, and linear inequalities.
In any optimization, problem involving a single inequality constraint, the LaGrange method can still be used and is quite simple. However, when more than one inequality constraint is involved, linear programming will be a better method. In fact, the linear programming technique differs from the classical optimization technique based on calculus, and it deals with optimization problem in which the optimizer faces inequality constraints, and where the constraints, as well as the objective function, are all linear rather than non-linear. For example, while making the purchase decision, the buyer is required to finance the expenditure out of his or her budgeted income, B. Thus:
Linear Programming (LP) is a mathematical method to determine the optimum allotment of scarce resources. LP can be applied practically in almost all aspects of business like Transportation & distribution, advertising & production planning and the like. Linear programming solves the objective functions which are to be optimized and is linear. As such, the relations between the variables which correspond to the resources will also become linear. This problem-solving method was first formulated and solved in the late 1940s. Seldom there is a novel mathematical technique being used with such a wide application as LP. In the present day, this theory is productively implemented to problems of capital budgeting, conservation of resources, economic growth prediction, and transportation systems. Of late LP has also helped to solve and unite many outstanding applications.
The most vital facet of a linear programming problem is to set it up appropriately for a manual or automated solutions. This calls for properly understanding the natures of the objective function and constraints so that their equations and inequalities may be well planned and formatted.
Problem-solving:
The Transportation Problem
Transportation models play a key role in logistics and supply chain management for decreasing cost and enhancing service. Therefore, the goal is to find the most cost-effective way to transport goods.
Let us consider a model with 2 origins and 2 destinations. The supply and demand at each origin (e.g.; warehouse) O1, O2 and destination (e.g.; market) D1 and D2, together with the unit transportation cost are summarized in the following table. ...Download file to see next pagesRead More
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