Please take a look at the problem in the picture. I attached it in this question.

5. For each of the statements below, state whether it is true or false. Justify your answer. (3) Consider the optimization problem min an) s.t. 9(3) 2 0. Suppose the current optimal objective value is 1:. Now, if I change the rightrhandside of the constraint from CI to 1 and resolve the problem, the new optimal objective value will be lei: than or equal to 0. Consider the following optimization problem: mina\" s.t. a: E X where re) is a nonconvex function and X is a nonempty set. Sup pose at a feasible solution m' E X, 112'} = 0, then so" must be a global optimal solution. Consider the following optimization problem (P) max Hm} s.t. 9,-(3) 2 hi, W E 1'. Suppose the optimal objective value of {P} is op. Then, the La grangian dual of (P) is given by (D) minffll : A 2 0}: (1} where ELK) = maxm) + 265! Aaliyah) b3}. Fhrthermore, sup pose the optimal objective value of (D) is up, then up 5 DD