Linear Programming. It is a method for selecting for selecting an optimum combination of factors from a series of inter-related alternatives each subjective to limitation. It involves the development of linear equations to obtain the best solution for the allocation problem. An allocation problem ".......arise whenever there are a number of activities to perform but limitations on either the amount of resources or the way they can be spent prevent us from performing each separate activity in the most effective way conceivable. In such situations we wish to allot the available resources to the activities in a way that will optimize the effectiveness".

Linear programming consists of:

(a)    The Simplex Method. This aims at maximizing or minimizing a given function subject to constraints in respect of each variable.

(b)   The Transportation Problem. This deals with the problems of matching the origins (stores, warehouses, factories) with the outlets (process centre market etc.) at minimum cost of distribution and transportation.

(c)    The Assignment Problem. It can handle the problems of assigning a given number of agents each one to the same number of takes so as to result in maximum efficiency or minimum cost.

Linear programming is an optimization technique. It is "a technique for specifying how to use limited resources or capacities of a business to obtain a particular objective such as least cost highest margin or least time when those resources have alternate uses." For example a manager has a given amount of resources for use (e.g., man-hours machine-time quantity of raw material etc.). The output per unit of resource used and the return per unit of output are known to the management would be to determine that resource combination which optimizes the goal of the firm (e.g., maximizing profit maximizing sales minimizing cost, etc.)

            The situations which require a search for "best" values of the variables subject to certain constraints are amenable to programming analysis. These situations cannot be handled by the usual tools of calculus or marginal analysis. The calculus techniques can only handle exactly equal constraints while this limitation does not exist in case of linear programming problem, e.g., a calculus problem might be formulated for a situation of minimizing cost subject to the constraint that exactly 500 units of total output were produced a corresponding linear programming problem would be formulated so as to minimize cost provided that no less than 500 units of total output were produced. Thus the linear programming technique has a much wider scope compared to the calculus or Lagrangian technique as the former can also be applied to those problem for which the latter cannot be used.

            A linear programming problem has two basic parts. The first part is the objective function which describes the primary purpose of the formulation to maximize some return (for example, profit) or to minimize some cost (for example production cost or investment cost). The second part is the constraint set. It is the system of equalities and/or inequalities, which describes the restrictions, include machine time man hours materials contract specification etc. equalities in the constraint set indicates that the resources described are to be fully used. Inequalities in the form of greater than (denoted by >) indicate that the total use of the resources must be more than the specified amount while inequalities in the form of less than (denoted by <) indicate that the total use of resources must be less than the given amount.

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