Place each of the following LPs in standard form and identify the corresponding A,

b, and c of definition 5.4 .

(a) min 4x1 + 2x2 - 33x3 s.t. x1 - 4x3 + x3 … 12 9x1 + 6x3 = 15

-5x1 + 9x2 Ú 3 x1, x2, x3 Ú 0

(b) max 45x1 + 15x3 s.t. 4x1 - 2x2 + 9x3 Ú 22

-2x1 + 5x2 - x3 = 1 x1 - x2 … 5 x1, x2, x3 Ú 0

(c) max 151x1 + 2x22 + 111x2 - x32 s.t. 3x1 Ú x1 + x2 + x3 0 … xj … 3 j = 1,c, 3

(d) max - 53x1 + 331x1 + 3x32 s.t. xj + 1 … xj + 1 j = 1, 2 a

3 j = 1 xj = 12 xj Ú 0 j = 1,c, 3

(e) min 2x1 + x2 - 4x3 s.t. x1 - x2 - 5x3 … 10 3x2 + 9x1 = -6 x1 Ú 0, x3 … 0

(f) min 4x1 - x2 s.t. -4x1 - x2 + 7x3 = 9

-x1 - x2 + 3x3 … 14 x2 … 0, x3 Ú 0