Minimization Consider the problem: minimize Z = 3x1 + 2x2 s.t x1 + 2x2 12 2x1 + 3x2 = 12 2x1 + x2 8 x1 0,x2 0 Solve this problem using the graphical method. Your answer should include a plot showing the constraints, feasible region, objective vector, and optimal point(s) and you should state the optimal solution including x1,x2, and Z. Note: We've provided blank plots at the end of the assignment you can optionally use when graphically solving problems. Summary of the steps in the graphical method: (a) Draw the boundary line for each constraint. You can put dashes on the side of the line where the constraint is satisfied to help visualize the inequality. (b) Find the feasible region where all constraints are satisfied. (c) Plot the gradient vector, Z = [dZ/dx1,dZ/dx2], by connecting the origin to the point (c1, c2) for objective Z = c1x1 + c2x2. If the coefficients are large you may need to scale them to plot the vector, ex. if Z = 120x1 + 80x2 you can draw a line to the point (3, 2) instead of (120, 80). (d) Lines perpendicular to the gradient are isoprofit lines where every point