# Linear Programming

### Linear programming is a mathematical way of planning, which involves three steps:

1. Identify the objective function as a linear function of its variables and state all the limitation on resources as linear equation and/ or inequalities (constraints).
2. Use mathematical techniques to find all possible sets of values of the variables (unknown) satisfying the constraints.
3. Select the particular set of values (obtained in 2) that lead to your objective – maximize profit, least cost etc.

- Helps in attaining optimum use of production factors.
- Can be used to solve allocation type problem.
- Can go a long in improving skills.
- Give possible and practical solution, subject to other constraints.
- Highlights bottle-hecks in production process.

Limitations of linear problem are:
- L.P models are based on the assumption of perfect divisibility of resources, accordingly the solution variables can have any value, where as some times some of the variables can have only integral value.
- Assumes linear relationship between variables, but many time in practice it is not possible to express both the objective function and the constraints in a linear form.
- Do not take into account effect of time.
- Can be adapted only under the condition of certainty.
- In case of large, complex and constrained problems computation problems are enormous.
- Deals only one single objective, but in real-life situations, there are more than one objective.

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