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Please help with the following problem:

Given a $m \times n$ matrix $A$, $m$-vectors $b$ and $y$, and $n$-vectors $c$ and $x$.
Write the dual $LP$ problems $P$ and $P^d$ in the standard form.

Whether $x$ (respectively, $y$) is a feasible vector for $P$ (respectively, for $P^d$)?
Whether $x$ (respectively, $y$) is an optimal solution for $P$ (respectively, for $P^d$)?
Whether the complementary slackness conditions hold for $P$ (respectively, for $P^d$)?

Consider the cases a-g listed below and explain your answers in each case.

a.) $ A = \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}$, $b^T = (8,18)$, $c^T = (2,1)$, $x^T = (6,0)$, $y^T = (0,2/3)$

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