Let PC Rn be a polyhedron. Then, there exist vectors x, x, k {2 Aix +...

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Let PC Rn be a polyhedron. Then, there exist vectors x¹, x², k {2 Aix² + Σ Oj v³ : №i ≥ 0₂ Σ di = 1, Oj ≥ 0, Σ A = 1, 0, ≥ 0}. i=1 j=1 i=1 and v¹, v²,..., v² in Rn such that P = (a) Construct an unbounded polyhedron in R2 which has exactly three distinct extreme points (say, x¹, x² and x³) and two extreme rays (say, v¹ and ²) and represent it in the above mentioned form. (b) Find a feasible point in this polyhedron that can be represented using scalars A₁, A2 and A3, and 0₁ and 02 that are all positive. Let PC Rn be a polyhedron. Then, there exist vectors x¹, x², k {2 Aix² + Σ Oj v³ : №i ≥ 0₂ Σ di = 1, Oj ≥ 0, Σ A = 1, 0, ≥ 0}. i=1 j=1 i=1 and v¹, v²,..., v² in Rn such that P = (a) Construct an unbounded polyhedron in R2 which has exactly three distinct extreme points (say, x¹, x² and x³) and two extreme rays (say, v¹ and ²) and represent it in the above mentioned form. (b) Find a feasible point in this polyhedron that can be represented using scalars A₁, A2 and A3, and 0₁ and 02 that are all positive.

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a Lets construct an unbounded polyhedron in R2 with 3 extreme points and 2 extre... View the full answer