5. For each of the statements below, state whether it is true or false. Justify your answer. (a) Consider the optimization problem min f(:1:) s.t. g(a:) 2 0. Suppose the current optimal objective value is 1:. Now, if I change the right-hand-side of the constraint from 0 to 1 and resolve the problem, the new optimal objective value will be less than or equal to o. (b) Consider the following optimization problem: min f(:1:)4 st. :1: E X where f(:13) is a nonconvex function and X is a non-empty set. Sup- pose at a feasible solution 33* E X, f(:13*) = 0, then 33* must be a global optimal solution. (c) Consider the following optimization problem (P) max it) s.t. g,(m)2b,-, WEI. Suppose the optimal objective value of (P) is '01:). Then, the La- grangian dual of (P) is given by (D) min{(z\\) ; A 2 0}, (1) where EON) = maxa,{f(a:) + 21.6,. A4945?) b,)}. Furthermore, sup- pose the optimal objective value of (D) is 119, then up 3 up