In a LPP, let \(R\) be the feasible region.
A. If R is unbounded then a max./min. value of objective function may not exist.
B. If R is bounded then a max. and min. value of objective function will always exist.
C. If a solution exists, it must occur at a corner point.
D. If R is bounded then max. will exist but min. may or may not exist for an objective function.
Choose the correct answer from the options given below:

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.