Following are three simplex matrices in various stages of the simplex method solution of a maximization problem.
(a) Identify the matrix for which multiple solutions exist. Circle the pivot and specify all row operations with that pivot that are needed to find a second solution.
(b) Identify the matrix for which no solution exists. Explain how you can tell there is no solution.
(c) For the remaining matrix, find the basic feasible solution. Use the variables x₁, x₂, . . . . . , the slack variables s₁, s₂, . . . , and the objective function f and tell whether these values give the optimal solution. If they do not, identify the next pivot.

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2 0 -4 1 0 0 1 -1 -6 0 -2 -1 1 3 A = 4 0 1 10 -3 0 -8 0 4 1 50 1 -2 12 4 1 20 B = 1 3 40 4 4 6 0 -를 1 170 1 2 0 1 40 0 1 0 C = -2 1 15 3 1 -1 1 4 60 0 0 0 4 0 6 1 220