Texts: (8 pt) Let X = {(x1, x2, x3) : x1 − 2x2 + 3x3 ≤ 3, x1, x2, x3 ≥ 0} ⊆ R³.
(a) Find all of the extreme points of X.
(b) Find all of the extreme directions of X. (Use normalization constraint, d₁ + d₂ + d₃ = 1.)
(c) Re-express X using an interior representation.
(d) Express x = (1, 0.5, 1)ᵀ as a convex combination of the extreme points of X and if necessary, as the nonnegative linear combination of the extreme directions of X.