Discussion
At any iteration of simplex method, if Δj (Zj - Cj) corresponding to any non-basic variable Xj is obtained as zero, the solution under the test is
Answer: C
If \(\Delta_{j} = Z_{j} - C_{j}\) for a non-basic variable \(X_{j}\) is zero at an iteration, the solution under test is an alternative solution, which is option (C). Bringing \(X_{j}\) into the basis changes the solution without changing the value of the objective function, so there are alternative optimal solutions.
A degenerate solution has a basic variable at zero, an unbounded solution has no limit on the improvement, and an optimal solution would be indicated by all the \(\Delta_{j}\) having the right sign. So (A), (B) and (D) are not what a zero \(\Delta_{j}\) shows.
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