Correct Answer - Option 3 : the primal objective value at x is less than the dual objective value at y

__Concept:__

Duality in Linear programming problem (LPP): It means a linear programming problem has another LPP which is derived from it.

**Original LPP is known as primal and derived LPP is known as Dual.**

Dual:

Dual can be found by using the below formula,

If primal is given as

Maximize CTx, subject to Ax ≤ b

Then dual will be

Minimize bTy, subject to A^{T}y ≥ c

If x is feasible for the primal, and y is feasible for the dual, then

**C**^{T}x ≤ b^{T}y

**That is primal objective is less than or equal to Dual objective.**

**At an optimal feasible solution, the primal objective is equal to the dual objective.**

**At a non-optimal feasible solution, the primal objective is less than the dual objective.**

If either the primal or the dual problem has a finite optimal solution, then the other problem also has a finite optimal solution.

If either problem has an unbounded optimum solution, then the other problem has no feasible solution at all