Consider the following problem: Minimize f(X) = x_1^2 + 2x_2^2 subject to: g_1(X): x_1^2 + x_2^2 lessthanorequalto 5 g_2(X): 2x_1-2x_2 lessthanorequalto 1 Suppose our task is to solve the above problem assuming g_2(X) is active at the optimal point. First solve it using graphical method. To do so, first you need to draw the objective function contours using Matlab. You may use the following Matlab commands to sketch the contours and constraint surfaces: %HW4P1 Matlab program for HW4 problem 1 close all [x1, x2] = meshgrid(-2.5: 0.1: 2.5): %Define grid for evaluation of "f" f = x 1.^2 + 2*x2.^2: % Define function "f" figure(1) v=[0.1: 0.5: 6]: % v = Range of contour values to plot [C, h]= contour(x1, x2, f, v): clabel(C, h) hold on ezplot('x1^2+x2^2 = 5') % Plot constraint surface g 1 (x) ezplot('2*xl - 2*x2 = 1') % Plot constraint surface g2(x) hold off grid minor Next, solve it using Karush-Kuhn-Tucker (KKT) conditions