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 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.
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