# Linearity Assumptions

- The doctrine characteristic of a difficulty that can be solved through linear programming technique is linearity. By linearity we entail that the difficulty which is to be studies through linear programming must be devised in terms of linear functions of two or more variables which are also subject to a group of linear restraints at least one of which must be articulated as inequality.

- That is, the difficulty to be scrutinised through linear programming is expressed as a whole in terms of linear equations and inequalities.

- It may be noted that the accurateness of the solution accomplished through linear programming is based on crucially upon the soundness of this presumption of linearity.

- The presumption of linearity makes the complicated arithmetical programming easier than it otherwise would have been.

- Linearity is not only merely simplifying presumption but also a pragmatic description of the actual world condition.

- The economic implications of linearity in the field of production are that invariable returns to scale prevail and average cost is invariable and resulting marginal products and average commodities parities.

- Pragmatic evidence has exposed that over a wide range of productivity, invariable returns to scale triumph and average cost curve is a horizontal over this variety.

- Apart from the implications of linearity presumption are that prices of inputs and productivity are provided for the industry.

- It is for the reason that of the invariable prices of inputs and productivity that they can also be exactly linear they may be so close to it that it may be warranted to make the linearity presumption.

__Objective Function__

- Objective function also called Criterion function, explains the determinants of the volume to be optimised or to be minimised.

- If the objective of an industry is to optimise productivities or profits, then this is the objective function of the industry.

- If the linear programming needs the minimisation cost then this is the objective function of the industry.

- An objective function has two classes – (1) the primal and (2) the dual. If the primal of the objective function is to optimise productivity subject cost expenditure, then its dual will be the minimisation of cost subject to a provided productivity.

__Restraints__

The optimisation of the objective function is subject to specified restrictions which are called restraints. The budget or earnings of a consumer is restraint on him for optimising his contentment.

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**Other topics under Theory of Production and Cost analysis:**

- Break Even and Leverage Analysis
- Concept of Cost
- Cost Volume Profit Analysis for Accomplishing Target Profits
- Elasticity of Supply and Its Function
- Establishment of Cost Function Analysis
- Establishment of Short Run Cost Function
- Estimation of Returns To Scale
- Isoquants, Equal Product Curves
- Linearity Assumptions and Choice of Product and Process
- Long Run average Cost Curve
- Optimum Input Combination
- Production Function with Two Variable Inputs
- Short Run Cost Function
- Survival Technique
- Theory of Production - Returns to One Variable Factor