Define linear programming and its importants and limitations??
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In this article we will discuss about Linear Programming (LP). After reading this article we will learn about: 1. Meaning of Linear Programming 2. Limitations of Linear Programming.
Meaning of Linear Programming:
LP is a mathematical technique for the analysis of optimum decisions subject to certain constraints in the form of linear inequalities. Mathematically speaking, it applies to those problems which require the solution of maximization or minimization problems subject to a system of linear inequalities stated in terms of certain variables.
If x and y, the two variables, are the function of z, the value of г is maximized when any movement from that point results in a decreased value of z. The value of z is minimized when even a small movement results in an increased value of z.
The term “linear” indicates that the function to be maximized is of degree one and the corresponding constraints are represented by a system of linear inequalities. The word “programming” means that the planning of activities in a manner that leads to some optimum results with limited resources. A programme is optimal if it maximizes or minimizes output, profits or cost of a firm.
Linear programming may thus be defined as a method to decide the optimum combination of factors (inputs) to produce a given output or the optimum combination of products (outputs) to be produced by given plant and equipment (inputs). It is also used by a firm to decide between varieties of techniques to produce a commodity.
Limitations of Linear Programming:
Linear programming has turned out to be a highly useful tool of analysis for the business executive. It is being increasingly made use of in theory of the firm, in managerial economics, in inter-regional trade, in general equilibrium analysis, in welfare economics and in development planning.
But it has its limitations:
1. It is not easy to define a specific objective function.
2. Even if a specific objective function is laid down, it may not be so easy to find out various technological, financial and other constraints which may be operative in pursuing the given objective.
3. Given a specific objective and a set of constraints, it is possible that the constraints may not be directly expressible as linear inequalities.
4. Even if the above problems are surmounted, a major problem is one of estimating relevant values of the various constant coefficients that enter into a linear programming mode, i.e., prices, etc.
5. This technique is based on the assumption of linear relations between inputs and outputs. This means that inputs and outputs can be added, multiplied and divided. But the relations between inputs and outputs are not always linear. In real life, most of the relations are non-linear.
6. This technique assumes perfect competition in product and factor markets. But perfect competition is not a reality.
7. The LP technique is based on the assumption of constant returns. In reality, there are either diminishing or increasing returns which a firm experiences in production.
8. It is a highly mathematical and complicated technique. The solution of a problem with linear programming requires the maximization or minimization of a clearly specified variable. The solution of a linear programming problem is also arrived at with such complicated method as the ‘simplex method’ which involves a large number of mathematical calculations.
9. Mostly, linear programming models present trial-and-error solutions and it is difficult to find out really optimal solutions to the various economic problems.
Meaning of Linear Programming:
LP is a mathematical technique for the analysis of optimum decisions subject to certain constraints in the form of linear inequalities. Mathematically speaking, it applies to those problems which require the solution of maximization or minimization problems subject to a system of linear inequalities stated in terms of certain variables.
If x and y, the two variables, are the function of z, the value of г is maximized when any movement from that point results in a decreased value of z. The value of z is minimized when even a small movement results in an increased value of z.
The term “linear” indicates that the function to be maximized is of degree one and the corresponding constraints are represented by a system of linear inequalities. The word “programming” means that the planning of activities in a manner that leads to some optimum results with limited resources. A programme is optimal if it maximizes or minimizes output, profits or cost of a firm.
Linear programming may thus be defined as a method to decide the optimum combination of factors (inputs) to produce a given output or the optimum combination of products (outputs) to be produced by given plant and equipment (inputs). It is also used by a firm to decide between varieties of techniques to produce a commodity.
Limitations of Linear Programming:
Linear programming has turned out to be a highly useful tool of analysis for the business executive. It is being increasingly made use of in theory of the firm, in managerial economics, in inter-regional trade, in general equilibrium analysis, in welfare economics and in development planning.
But it has its limitations:
1. It is not easy to define a specific objective function.
2. Even if a specific objective function is laid down, it may not be so easy to find out various technological, financial and other constraints which may be operative in pursuing the given objective.
3. Given a specific objective and a set of constraints, it is possible that the constraints may not be directly expressible as linear inequalities.
4. Even if the above problems are surmounted, a major problem is one of estimating relevant values of the various constant coefficients that enter into a linear programming mode, i.e., prices, etc.
5. This technique is based on the assumption of linear relations between inputs and outputs. This means that inputs and outputs can be added, multiplied and divided. But the relations between inputs and outputs are not always linear. In real life, most of the relations are non-linear.
6. This technique assumes perfect competition in product and factor markets. But perfect competition is not a reality.
7. The LP technique is based on the assumption of constant returns. In reality, there are either diminishing or increasing returns which a firm experiences in production.
8. It is a highly mathematical and complicated technique. The solution of a problem with linear programming requires the maximization or minimization of a clearly specified variable. The solution of a linear programming problem is also arrived at with such complicated method as the ‘simplex method’ which involves a large number of mathematical calculations.
9. Mostly, linear programming models present trial-and-error solutions and it is difficult to find out really optimal solutions to the various economic problems.
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