Determine whether the feasible set for each of the following systems of constraints is convex, and if not, indicate points x112 and x122 that violate definition 3.27 .

(a) 1x122 + 1x222 Ú 9 x1 + x2 … 10 x2, x2 Ú 0

(b) 1x122>4 + 1x222 … 25 x1 … 9 x1 + x2 Ú 3 x1, x2 Ú 0

(c) x1 - 2x2 + x3 = 2 x1 + 8x2 - x3 … 16 x1 + 4x2 - x3 Ú 5 x1, x2, x3 Ú 0

(d) a 12 j = 1 3xj … 50 xj Ú xj - 1 j = 2,c, 12 xj Ú 0 j = 1,c, 12

(e) x1 + 2x2 + 3x3 + x4 … 24 0 … xj … 10, j = 1,c, 4 xj integer, j = 1,c, 4

(f) a 50 j = 1 xj … 200 xj … x1 j = 2,c, 100 xj Ú 0 j = 1,c, 100 x1 = 0 or 1