1. Nonlinear Optimization (45 points) For the following problem min x + x2 a) Set up...

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1. Nonlinear Optimization (45 points) For the following problem min x + x2 a) Set up the KKT conditions s. t. x1 + x2 1.5 x12-2x20 b) Solve the problem by checking the four options a. Both constraints binding b. First constraint binding, second non-binding c. First constraint non-binding, second binding d. Both constraints non-binding c) Which ones are feasible solutions to the optimization problem? For each one which is not a feasible solution, give an explanation why it is not a feasible solution. d) Which one is the optimal solution? 1. Nonlinear Optimization (45 points) For the following problem min x + x2 a) Set up the KKT conditions s. t. x1 + x2 1.5 x12-2x20 b) Solve the problem by checking the four options a. Both constraints binding b. First constraint binding, second non-binding c. First constraint non-binding, second binding d. Both constraints non-binding c) Which ones are feasible solutions to the optimization problem? For each one which is not a feasible solution, give an explanation why it is not a feasible solution. d) Which one is the optimal solution?