Simplex Negative Zj Cj
1. The problem asks about the meaning of a negative $Z_j - C_j$ value in a simplex table during a maximization problem.
2. In the simplex method, $Z_j$ represents the total contribution to the objective function from variable $j$, and $C_j$ is the coefficient of variable $j$ in the objective function.
3. The difference $Z_j - C_j$ (often called the reduced cost) indicates how much the objective function will improve if that variable enters the basis.
4. If $Z_j - C_j$ is negative in a maximization problem, it means that increasing that variable can improve the objective function value.
5. Therefore, a negative $Z_j - C_j$ shows there is room for improvement, and the current solution is not yet optimal.
Answer: b. There is room for improvement