1. Nonlinear Optimization (45 points) For the following problem min x12 + x; s. t. x1 + x2 5 1.5 x12 2x2 5 0 a) Set up the KKT conditions 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. (1) Which one is the optimal solution