Question: Question 4 (25 Points) Consider the following NLP (the same model in question 3): maxf(x1,x2)=2x1x21+6x23x22s.t.4x1+x224(1)x1+2x212(2)x1,x20(3)maxf(x1,x2)=2x1x12+6x23x22s.t.4x1+x224(1)x1+2x212(2)x1,x20(3) Perform one iteration of the modified simplex algorithm to solve

Question 4 (25 Points)

Consider the following NLP (the same model in question 3):

maxf(x1,x2)=2x1x21+6x23x22s.t.4x1+x224(1)x1+2x212(2)x1,x20(3)maxf(x1,x2)=2x1x12+6x23x22s.t.4x1+x224(1)x1+2x212(2)x1,x20(3)

Perform one iteration of the modified simplex algorithm to solve this problem. Clearly provide the KKT conditions, show how you manipulate them to obtain the related linear programming formulation, and identify the additional complementarity constraints that are enforced by the algorithm. Write down the list of candidate entering variables, the selected entering variable, and the leaving variable clearly.

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