18 moints) Consider the following linear programming problem Max z = -x + 3x s.t. X1 + X2 S8 (1) Xi - X2 S 2 X2SS (3) X1, X220 (4) & (5) (a) (2 point) Graph the constraints, feasible set, and the gradient of the objective function. ha point) Use the graphical solution technique to determine the optimal solution. Clearly show the optimal point on the graph. What is the value of the objective function at optimum? (c) (1 point) How the gradient of the objective function changes of the coefficient of x2 decreases? What is the change to gradient? (d) (2 point) If we add one more objective function MIN 22X1 - 3x2 Graph the gradients of the obiective functions & determine the improvement cone. Plot the improvement cone at all extreme (comer) points of the feasible set. (e) (1 point) Determine the efficient frontier. (1 point) Determine the composite objective function for the weighting method with weights we =2&w =8