Duality in LP problem

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Duality in LP problem

All linear programming problems have another problem associated with them, which is known as its dual. In other words, every minimization problem is associated with a maximization problem and vice-versa. The original linear programming problem is known as primal problem, and the derived problem is known as its dual problem. The optimal solutions for the primal and dual problems are equivalent.Conversion of primal to dual is done because of many reasons. The dual form of the problem, in many cases, is simple and can be solved with ease. Moreover, the variables of the dual problem contain information useful to management for analysis.
Example ; Construct the dual to the primal problem.
2x1 + 8x2
60
3x1 + 5x2
45
5x1 – 6x2
10
x2
40
where,
x1, x2
0
Solution:
Minimize      W = 60y1 + 45y2 + 10y3 + 40y4
Subject to constraints,
2y1 + 3y2 + 5y3 + 0y4   6
8y1 + 5y2 + 6y3 + y4  10
where,   y1, y2, y3, y4   0