Limitations of linear programming are as follows:
Although LP is an improvement over conventional theory of production yet it is not free from limitations LP is an important technique of planning.
But the real problems of planning cannot be solved directly by L P. because it has certain limitations and these are following:
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1. To specify an objective function in mathematical form is not an easy task.
2. Even if objective function is determined, it is difficult to determine social, institutional, financial and other constraints.
3. It is also possible that the objective function and constraints may not be directly specified by linear in equality equations.
4. To determine the relevant values of the co-efficient of constraints involved in LP is a main problem.
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5. The assumptions of LP are also unrealistic. It assumes that factory proportion remains constant. In addition for it, the relationship between input and output, production and cost, and production and total revenue are assumed to be linear.
All these assumptions imply constant returns to scale and perfect competition in the market. But in fact the relations are not always linear and imperfect competition prevails in the market.
6. It is a very complex method as it uses mathematical techniques extensively. LP models presents a trial and error solutions and it is difficult to find out really optimal solutions to various business problems.
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7. Under linear programming to increase production by a single process the quantity of all inputs is to be increased in a fixed proportion.
But the production of a number of goods can be increased to some extent by increasing only one or two inputs. It means that production can be increased to some extent by varying factors proportion.
In spite of these limitations LP is extensively used in taking business decisions. Most of the limitations of LP can be solved by utilizing the services of mathematicians. The above limitation can be removed by developing nonlinear programming techniques.
