The main objective behind using linear programming is to help identify best allocation of various company resources. When it is referred as the allocation process, then it is certain to include resources like money, material, manpower, and machines etc. that can finally specify activities and also optimize the objectives.
Through linear programming it is also possible to attain the maximum use of any productive factors which can finally help in enhancing decision making quality. With the help of linear programming you can easily highlight bottlenecks in regard to production processes.
While analyzing the primal or dual pair you will get to know about different properties related to problem formulation:
The standard form of LPP
Suppose, x1, x2, ……xn turns out to be decision variables in case of general LPP. So, it is important to determine values of different variables such as:
Maximize z = c1 x1 + c2 x2 + …..+ cn xn
Subject to the constraints:
a11 x1 + a12 x2 + …….. + a1n xn = b1
a21 x1 + a22 x2 + …….. + a2n xn = b2
am1 x1 + am2 x2 + …….. + amn xn = bm
x1, x2, …, xn ≥ 0.
When a linear programming problem is written in such a form then it is said to have standard form. This can further be solved through simplex method.
While discussing about primal or dual problem, it is identified that both shares relationship in regard to solution:
While discussing about simplex method in LPP, it is important to identify that each and every linear program can easily be converted into standard form
In standard form the objective is maximized and constraints become equals as well as variable turn out to be non-negative.
This can be performed in the following manner:
In case the constraint is , then certainly convert into equality constraint just by subtracting any non-negative surplus variable .