Please help with number c, there's no references!

b) Suppose the following tableau was obtained in the course of solving a linear program with nonnegative variables x1, x2, x3 and two inequalities. The objective function is maximized and slack variables S1 and S2 were added. Z X1 X2 X3 S1 S2 RHS 1 0 a 0 4 82 0 0 -2 w NC 1 3 0 1 - 1 3 0 -5 3 Give the conditions on a, b and c that are required for the following statements to be true: i. The current basic solution is a feasible basic solution. ii. The current basic solution is optimal. 2 Page SSOA021 ASSIGNMENT 1 2021 c) In a minimization problem with some "=" and ">" constraints the following tableau is obtained, where Ai's represent the artificial variables and Si's represent the slack/surplus variables. C1 2 1 0 0 12 M/4+2 1/4 3/4 5/4 AL 0 1 0 0 A2 -5M/4+1 -1/4 0 1 0 82 M/4-1 1/4 -1/4 1/4 93 0 3M/2+6 0 3/2 0 3/2 1 3/2 0 0 1/4 -1/4 Find the optimal solution for this problem. Identify and motivate the special case involved, if any. d) Consider the following LP