please answer (5,2)

Consider the following linear programming problem in standard form: (P) min{ch: A3: = b, :1: 2 0}, Where A E Rm\(5.1) Suppose that there exists a nonbasic variable 933' whose reduced cost is equal to 0, i.e., there exists an index j E N such that 53' = 6:; C(AB)_1Aj = 0. Prove that (P) has an innite number of optimal solutions. [1 mark] (5.2) Using (5.1) and one of the previous problems in the exercise sets, prove the following result: 93* is the unique optimal solution of (P) if and only if the reduced costs of all nonbasic variables are strictly positive, i.e., a = cj cg(AB)1Aj > 0, j e N