 Solution

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

x, y

, nonnegativity gives

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

The first inequality uses

A^{T} y \geq c

and

x \geq 0

A x \leq b

and

y \geq 0

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