Problem 4 Let f : R2 -> R. Consider the problem minimize f(x) s.t. X1, X2 2 0 where a = (21, 12) . Suppose that Vf(0) # 0, and of (0) So, of (0) SO Show that 0 cannot be a minimizer for this problem. Problem 5 Let c E R", c # 0, and consider the problem of minimizing the function f(x) = c x over a constraint set A' C R" . Show that we cannot have a solution lying in the interior of X' . Problem 6 Consider the problem maximize C1 1 + C2 2 s.t. *1 +22 1. X1, X2 2 0 where ci and c2 are constants such that c1 > C2 2 0. This is a linear programming problem. Assuming that the problem has an optimal feasible solution, use the FD-FONC to show that the unique optimal feasible solution a* is (1, 0) T