Convert each of the following multiobjective optimization models to a goal program seeking the specified target levels, and minimizing the unweighted sum of all goal violations.

(a) min 3x1 + 5x2 - x3 max 11x2 + 23x3 s.t. 8x1 + 5x2 + 3x3 … 40 x2 - x3 … 0 x1, x2, x3 Ú 0 Targets 20,100.

(b) min 17x1 - 27x2 max 90x2 + 97x3 s.t. x1 + x2 + x3 = 100 40x1 + 40x2 - 20x3 Ú 8 x1, x2, x3 Ú 0 Targets 500, 5000.

(c) max 40x1 + 23x2 min 20x1 - 20x2 min 5x2 + x3 s.t. x1 + x2 + 5x3 Ú 17 40x1 + 4x2 + 33x3 … 300 x1, x2, x3 Ú 0 Targets 700, 25, 65.

(d) max 12x1 + 34x2 + 7x3 min x2 - x3 min 10x1 + 7x3 s.t. 5x1 + 5x2 + 15x3 … 90 x2 … 19 x1, x2, x3 Ú 0 Targets 600, 20, 180.

(e) min 22x1 + 8x2 + 13x3 max 3x1 + 6x2 + 4x3 s.t. 5x1 + 4x2 + 2x3 … 6 x1 + x2 + x3 Ú 1 x1, x2, x3 = 0 or 1 Targets 20, 12.

(f) min 4x2 + ln1x22 + x3 + ln1x32 max 1x122 + 91x222 - x1 x2 s.t. x1 + x2 + x3 … 10 4x2 + x3 Ú 6 x1, x2, x3 Ú 0 Targets 20, 40.