) Solve the following LP problems using the graphical method. For each problem, clearly indicate (i) the feasible region, (ii) the improving direction, (iii) the exact coordinates of optimal solution x through solving the corresponding system of equations (identify all optimal solutions if there exist multiple), (iv) and the optimal objective value , and (v) why the optimal solution does not exist if that is the case (infeasible or unbounded). (a) max = x1 + 4x2 s.t. x1 + x2 3 x1 + 3x2 1 x1 + x2 2 x1, x2 0. (b) max = 3x1 + 9x2 s.t. x1 + 3x2 160 2x1 + x2 120 x1 45 x1, x2 0. (c) max = 3x1 + 2x2 s.t. 2x1 + 2x2 3 x1 + 2x2 1 x1 + x2 1 x1, x2 0