Consider a linear program with feasible region CR, objective f(x) = ca, and feasible point y...

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Consider a linear program with feasible region CR", objective f(x) = ca, and feasible point y = int(2). Provide an algorithm for finding a unit-length direction vector d R", derived from any randomly-generated vector wR", which satisfies y+ad int() and cd <0 for some a > 0. Explain why such an algorithm could be useful in an interior-point method scenario. Consider a linear program with feasible region CR", objective f(x) = ca, and feasible point y = int(2). Provide an algorithm for finding a unit-length direction vector d R", derived from any randomly-generated vector wR", which satisfies y+ad int() and cd <0 for some a > 0. Explain why such an algorithm could be useful in an interior-point method scenario.