Question

In the final simplex tableau, a zero C_j-Z_j entry for a nonbasic variable indicates that the problem has :

• A. Unique Solution
• B. Multiple Optimal Solutions
• C. Unbounded Solutions
• D. Infeasible Solution

Hint:

Zero Cj-Zj for a nonbasic variable in the optimal tableau means an alternative optimum exists.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:

• In the simplex method, the Cj-Zj row shows how much the objective function would change if one unit of a nonbasic variable entered the solution.

Step 2: Detailed Explanation:

• At the optimal tableau, a nonbasic variable with a non-zero Cj-Zj changes the objective value if it enters, so the optimum is unique.

• If a nonbasic variable has Cj-Zj equal to zero, bringing it into the basis gives another corner point with the same objective value. This means there is an alternative optimal solution.

• Unboundedness and infeasibility are found by other signs (no positive ratio, or artificial variables remaining in the basis), not by a zero Cj-Zj.

Step 3: Final Answer:
The correct option is (B) Multiple Optimal Solutions.