Duality Theorem. An example where the dual is feasible but the primal is not

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Can anyone provide an example where dual is feasible but the primal is not? This is a linear programming question.

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Primal: $$\min_x \{0 : 0x \geq 1, x \geq 0\}$$ Dual: $$\max_y \{ y : 0y \leq 0, y \geq 0\}.$$