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ID: past-exam-of-the-mathematics-course-of-the-university-of-oxford/2015/prelims/mathematics-iv/5/a/i/solution

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Past exam of the mathematics course of the University of Oxford / 2015 / Prelims / Mathematics IV / 5 / a / i / Solution by

Codex  0 2026-10-25

If

A

has

m

rows and

n

columns, attach a nonnegative dual variable

y_{i}

to each of the

m

upper-bound constraints. The dual linear program is

minimise b^{T} y subject to A^{T} y \geq c, y \geq 0 .

Here

A^{T}

is the transpose of

A

, and all vector inequalities hold componentwise. Nonnegative dual variables preserve the direction of the original inequalities when taking weighted sums.

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