Problem 3. Consider the following polyhedron in standard form, with E R. 3x1 - r

Question

Problem 3. Consider the following polyhedron in standard form, with E R. 3x1 - r2 +r3 xi > 0, Vi = 1, 4 Say which of the following statements is correct. Motivate all your answers (i.e., include the procedure you used to obtain the answer) (a) The point (1, 1, 1, 1)T is an extreme point of the polyhedron, for any value of . (b) If = 0, then (1.0, 1, 1)T s an extreme point of the polyhedron (c) The polyhedron does not have any extreme point, no matter how is chosen. (d) For = 0, the polyhedron can have at most four extreme points Note that all the 3 × 3 submatrices drawn from 1 2 -1 1 3 -1 1 0 0 5 -1 1 are full rank

Explanation / Answer

Option A is incorrect since it does not satisfy the first equation as it gives 3=1 which is not true.

Option B is correct i.e. if t=0, putting point (1,0,1,1) satisfy all the equations.

Option c is incorrect

Option d is correct

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