Question 1: Consider the nonlinear optimization problem min 2x + x2 + 5x3 + x1 x3 X1x2 + x1 - x3 subject to x + x X3 3. Q1.a Is the point (1, 2,5) an optimal solution of the problem? Q1.b Are the necessary conditions of optimality also sufficient conditions for this problem? Q1.c Does the Lagrangian of this problem have a saddle point? If so, which is it? Q1.d What is the optimal value and the optimal solution of the dual problem? Q1.e Calculate a subgradient of the dual function at the point (0,1)