For each of the following LPs and solution vectors, demonstrate that the given solution is feasible, and

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For each of the following LPs and solution vectors, demonstrate that the given solution is feasible, and compute the bound it provides on the optimal objective function value of the corresponding dual.

(a) min 30x1 + 2x2 and x = 12, 52 s.t. 4x1 + x2 … 15 5x1 - x2 Ú 2 15x1 - 4x2 = 10 x1, x2 Ú 0

(b) max 10x1 - 6x2 and x = 10, 22 s.t. 12x1 + 4x2 … 8 3x1 - x2 Ú -5 2x1 + 8x2 = 16 x1, x2 Ú 0

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