Consider the linear programming problem (LPP) :
Maximize \(Z=6 x+3 y\)
subject to the conditions
\(4 x+y \geq 80\)
\(x+5 y \geq 115\)
\(3 x+2 y \leq 150\)
\(x \geq 0, y \geq 0\)
In reference to the above LPP, which of the following are correct?
(A) The feasible region is bounded.
(B) The corner points of the feasible region are (15,20), (40,15) and (0,75).
(C) The maximum value of the objective function is 285.
(D) The LPP does not have optimal solution.
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.