Graphically, find the optimum design variable x_1 and x_2 and evaluate the function at this optimum point, for the following optimization problem. You may do this problem by hand with pencil and paper or use Matlab to generate the plots necessary (suggested). Feel free to check your answer using Matlab's fmincon function. min x_1,x_2 f(x_1,x_2) = x_1 + 2x_2 subject to: 2x_1 + x_2 4 x_1,x_2 0 2. Graphically, find the optimum design variable x_1 and X_2 and evaluate the function at this optimum point, for the following optimization problem. You may do this problem by hand with pencil and paper or use Matlab to generate the plots necessary (suggested). Feel free to check your answer using Matlab's fmincon function. max x_1x_2 f(x_1,x_2) = 4x_1x_2 subject to: x_1 + x_2 20 x_2- x_1 10 3. Graphically, find the optimum design variable x_1 and x_2 and evaluate the function at this optimum point, for the following optimization problem. You may do this problem by hand with pencil and paper or use Matlab to generate the plots necessary (**highly suggested**). Feel free to check your answer using Matlab's fmincon function. min x,y f(x, y) = 9x^2 + 13y^2 + 18xy - 4 subject to: x^2 + y^2 + 2x = 16