A small company manufactures necklaces and bracelets. The combined number of necklaces and bracelets it can handle per day is at the most 24 .A bracelet takes 1 hour to make and a necklace takes half hour to be made.Maximum number of hours available per day is 16 .If the number of necklaces and bracelets made per day is \(x\) and \(y\)
respectively then the time constraint for the L.P.P.is :

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.