Solve the following LP problems using the graphical method. For each problem, clearly indicate (i) the feasible region, (ii) the optimal solution x* (identify all optimal solutions if there exist multiple) and the optimal objective value zeta*, and (iii) why the optimal solution does not exist if that is the case. max zeta = x_1 + 3x_2 s.t x_1 + x_2 greaterthanorequalto 2 -x_1 + x_2 lessthanorequalto 1 x_1 + 2x_2 lessthanorequalto 6 x_1, x_2 greaterthanorequalto 0