# Let x be a non-optimal feasible solution of a linear programming maximization problem and y a dual feasible solution, then

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Let x be a non-optimal feasible solution of a linear programming maximization problem and y a dual feasible solution, then
1. the primal objective value of x is greater than the dual objective value at y
2. the primal objective value at x can be equal to the dual objective value at y
3. the primal objective value at x is less than the dual objective value at y
4. the dual can be unbounded

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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 ATy ≥ c

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

CTx ≤ bTy

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