Problem 2. (30 points) Consider the linear optimization problem maxcTx Ax = b, x 0 s.t. where c (2019,2, 1,4, 10)T and b (1,2). 13 61 0 A=(2 4 801 (a) What is the rank of A? (b) True or false: The set (2019,2) is a basis. (c) True or false: The set (2,3 is a basis. (d) True or false: (e) True or false: The set [1,4) is a basis. (D Find the dictionary for basis (1.2). The set (1,2,3 is a basis s (1,2). (g) What is the precise relationship between degeneracy, cycling, and the lexico- graphic method