Estimate a range for the optimal objective value for the following LPs:

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(a) Minimize z = 5x1 + 2x2 subject to x1 - x2 Ú 3 2x1 + 3x2 Ú 5 x1, x2 Ú 0

(b) Maximize z = x1 + 5x2 + 3x3 subject to x1 + 2x2 + x3 = 30 2x1 - x2 = 40 x1, x2, x3 Ú 0

(c) Maximize z = 2x1 + x2 subject to x1 - x2 … 2 2x1 … 8 x1, x2 Ú 0

(d) Maximize z = 3x1 + 2x2 subject to 2x1 + x2 … 3 3x1 + 4x2 … 12 x1, x2 Ú 0