Consider the following NLP: 2x+2x12+x10x - 1022 max s.t. x+x5 3x1 + x 6. I1,...

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Consider the following NLP: 2x+2x₁12+x²10x₁ - 1022 max s.t. x+x≤5 3x1 + x₂ ≤ 6. I1, I2 20 (a) Aside from regularity and the given constraints, what are the first order necessary conditions for this problem? (Be as specific as possible.) (b) Find a solution by assuming the first Lagrangian multiplier constraints is active and the second one is inactive. (c) Does this satisfy the first order necessary conditions? Explain. Consider the following NLP: 2x+2x₁12+x²10x₁ - 1022 max s.t. x+x≤5 3x1 + x₂ ≤ 6. I1, I2 20 (a) Aside from regularity and the given constraints, what are the first order necessary conditions for this problem? (Be as specific as possible.) (b) Find a solution by assuming the first Lagrangian multiplier constraints is active and the second one is inactive. (c) Does this satisfy the first order necessary conditions? Explain.