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}$, $b^T = (8,18)$, $c^T = (2,1)$, $x^T = (6,0)$, $y^T = (0,2/3)$