Consider the cone C = {x = R | a'x 0, i = 1,...,m} and assume...

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Consider the cone C = {x = R | a'x 0, i = 1,...,m} and assume that the first n constraint vectors a,..., an are linearly independent. For any nonnegative scalar r, we define the polyhedron P, by P = { x =C | x=r} i=1 (a) Show that the polyhedron P, is bounded for every r 0. (b) Letr> 0. Show that a vector x P, is an extreme point of P, if and only if x is an extreme ray of the cone C. Consider the cone C = {x = R | a'x 0, i = 1,...,m} and assume that the first n constraint vectors a,..., an are linearly independent. For any nonnegative scalar r, we define the polyhedron P, by P = { x =C | x=r} i=1 (a) Show that the polyhedron P, is bounded for every r 0. (b) Letr> 0. Show that a vector x P, is an extreme point of P, if and only if x is an extreme ray of the cone C.

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a To show that the polyhedron Pr is bounded for every r geq 0 Since x in C we have aix geq 0 for i 1 ... View the full answer