5. For each of the statements below, state whether it is true or false. Justify your answer. (a) {Cl Consider the optimization problem min x) s.t. 91m) 2 0. Suppose the current optimal objective value is 1:. Now, if I change the rightrhandside of the constraint from 0 to 1 and resolve the problem, the new optimal objective value will be less than or equal to 2:. Consider the following optimization problem: minf(:r}4 s.t. a: e X where at) is a nonconvex function and X is a nonempty set. Sup pose at a feasible solution cc\" E X, f(:s"'} = 0, then cc" must be a global optimal solution. Consider the following optimization problem (P) max Hm} s.t. 92(3) 2 hi, W E I. Suppose the optimal objective value of (P) is up. ThenI the La grangian dual of (P) is given by (D) minus) : A 33 0}: (1) where 9.) = maxm) + Zia Ai(g,g(a:) 55)}. Furthermore, sup- pose the optimal objective value of {D} is up, then up 5 \"U D