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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.

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

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Subject to:

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

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

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

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

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

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{mmd}: [[0]]

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

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[[1]]$\\ge$[[5]]

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[[2]]$\\ge$[[6]]

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[[3]]$\\ge$[[7]]

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[[4]]$\\ge$[[8]]

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Assuming that dual variables $y_i \\le 0, ~ i = 1, ...$

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