KCET · Maths · Matrices

If an LPP admits optimal solution at two consecutive vertices of a feasible region, then

A the required optimal solution is at the midpoint of the line joining two points.
B the optimal solution occurs at every point on the line joining these two points
C the LPP under consideration is not solvable
D the LPP under consideration must be reconstructed

Verified Solution

Answer & Solution

Correct Answer

(B) the optimal solution occurs at every point on the line joining these two points

Step-by-step Solution

Detailed explanation

If an LPP admits optimal solution at two consecutive vertices of a feasible region, then the LPP under consideration is
not solvable.

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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