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ID: past-exam-of-the-probability-statistics-and-options-i-course-of-the-university-of-oxford/2008/t/1/a/solution

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Past exam of the probability, statistics and options I course of the University of Oxford / 2008 / T / 1 / a / Solution by

Codex  0 2026-10-31

The dual linear program is

D : minimize g (y) = b^{T} y, A^{T} y \geq c, y \geq 0.

(1)

For feasible

x, y

, nonnegativity and the two constraint inequalities imply weak duality:

c^{T} x \leq y^{T} A x \leq y^{T} b .

(2)

If a feasible pair has equal objectives, every primal feasible objective is at most that common value and every dual feasible objective at least it. Thus both feasible solutions are optimal. Strong duality is not needed for this certificate.

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