Question

what is meant by dual and primal problems in linear programming.

Answer 1

Ans:

The Duality in Linear Programming states that every linear programming problem has another linear programming problem related to it and thus can be derived from it. The original linear programming problem is called “Primal,” while the derived linear problem is called “Dual.

The concept of Duality can be well understood through a problem given below:

Maximize

Z = 50x1+30x2

Subject to:
4x1 + 3x2 ≤ 100
3x1 + 5x2 ≤ 150
X1, x2 ≥ 0

The duality can be applied to the above original linear programming problem as:

Minimize

G = 100y1+150y2

Subject to:

4y1 + 3y1 ≥ 50
3y1 +5y2 ≥ 30
Y1, y2 ≥ 0