Problem 1 Consider the following 2D function: f(x, x) = x + xx + 2x +5 Suppose an iterative method manages to optimize this function with two steps, starting with an initial design at x = (3,2). In the first step, the search direction is d= (-1,-1) and the step size is a = 1.0. In the second step, the search direction is d = (-1,-0.5) and the step size is a = 2.0. a) Calculate the design variable and objective function values for each step, i.e., x, x, and x and f(x), f(x), and f(x). (40%) b) Use MATLAB to plot the contour of this function and add labels to the contour lines. Then, plot the locations of x0, x, and x as symbols and connect them with solid lines to show the trajectory of optimization process. Finally, use the text command to annotate the locations for x, x, and x2 in the plot. Attach the plot to the solutions and upload the MATLAB code to Canvas. (60%)