(Solved): Problem 3 Solve this problem using Matlab. Example 3.12 (Problem using Lagrangian) Minimize: f(x)=x ...

Problem 3 Solve this problem using Matlab. Example 3.12 (Problem using Lagrangian) Minimize: $$f(\mathbf{x})=x_1^2+x_2^2$$ Subject to: $$h(\mathbf{x})=2x_1+x_2?2=0$$ Normally, we would use the equality constraint to eliminate a design variable from the objective function. However, here we will solve the problem using Lagrange Multipliers. Let us form the Lagrangian function and solve the problem that way. The Lagrangian is : $$L(\mathbf{x},?)=f(\mathbf{x})+?h(\mathbf{x})=x_1^2+x_2^2+?\left(2x_1+x_2?2\right)$$ At the optimum. $$\frac{?L(\mathbf{x},?)}{?x_i}=\frac{?f(\mathbf{x})}{?x_i}+?\frac{?h(\mathbf{x})}{?x_i}=0$$ or $$\begin{array}{l}\frac{?L(\mathbf{x},?)}{?x_1}=2x_1+2?=0\\ \frac{?L(\mathbf{x},?)}{?x_2}=2x_2+?=0\end{array}$$