QUESTION 1 (20 marks) Consider a minimization linear program of the form "minimize c"'x, subject to Ar = b, x 2 0", with the following given data: 0 0 -1 -1 1 1 A = -1 2 0 1 10 b 1 0 0 -31 1 = [ -2 6 2 4 1 -1 ]T (a) Apply the revised simplex method using Bland's rule to get an optimal solution to the linear program, starting from a feasible basis JB = {$3, Is, I6} and the corresponding basic feasible solution is a* = 0, 0, 2, 0, 1, 2]. The inverse of the basic coefficient matrix equals B-1 (b) Starting from the optimal basis obtained from Part (a), determine the range of values that the objective coefficient of z; can take to remain the optimality of the basis. (c) Suppose a new variable is added, denoted by co. The constraint coefficient vector of the newly added variable To is do = [1 2 0]T. Starting from the optimal basis obtained from Part (a), determine the range of values that the objective coefficient of the newly added variable, denoted by co, can take to remain the optimality of the basis