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Formulating duality problems

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Given LP problem: optimise $cx$ subject to constraints $Ax \\le/\\ge b,$ formulate the dual problem.

{mm}: $\\simplify {{c[0]}x_1+{c[1]}x_2+{c[2]}x_3+{c[3]}x_4+{c[4]}x_5} $

Subject to:

$\\simplify {{a1[0]}x_1+{a1[1]}x_2+{a1[2]}x_3+{a1[3]}x_4+{a1[4]}x_5} = \\var{b[0]}$

$\\simplify {{a20}x_1+{a21}x_2+{a22}x_3+{a23}x_4+{a24}x_5} \\le \\var{b[1]}$

$\\simplify {{aa1[0]}x_1+{aa1[1]}x_2+{aa1[2]}x_3+{aa1[3]}x_4+{aa1[4]}x_5} \\ge \\var{b[2]}$

$\\simplify {{aa2[0]}x_1+{aa2[1]}x_2+{aa2[2]}x_3+{aa2[3]}x_4+{aa2[4]}x_5} = \\var{b[3]}$

$\\simplify {{aa3[0]}x_1+{aa3[1]}x_2+{aa3[2]}x_3+{aa3[3]}x_4+{aa3[4]}x_5} \\ge \\var{b[4]}$

$\\simplify {{aa4[0]}x_1+{aa4[1]}x_2+{aa4[2]}x_3+{aa4[3]}x_4+{aa4[4]}x_5} \\le \\var{b[5]}$

$x_1,x_2,x_3,x_4,x_5 \\ge 0$

Formulate the dual problem (use variables \"y1,y2,...\" for $y_1,y_2,...$, and \">=\" or \"<=\" for $\\ge$ or $\\le$)

assuming that dual variables $y_2,y_6 \\le 0$ and $y_3,y_5 \\ge 0$:

{mmd}: [[0]]

Subject to (express constraints in the form $A^T y \\ge c$):

[[1]]$\\ge$[[6]]

[[2]]$\\ge$[[7]]

[[3]]$\\ge$[[8]]

[[4]]$\\ge$[[9]]

[[5]]$\\ge$[[10]]

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